Honestly, I don't see what it adds. I'm not trying to be obtuse, but, having read several different aspects of lightsabers, combat and history, I don't think it adds to the lore. You're doing a great job of trying to explain it and how you like it, but it isn't clicking for me.
The Inquisitors almost certainly since, again in the Ahsoka novel, it's said that
"Lightsaber construction was a Jedi art of the highest order." which presumably also applies to Sith and seems to be backed up by Vader's line to Luke in RotJ. It's no coincidence that it is among the final trials for a Initiate to become a Padawan.
Inquisitors seem to only get the barest minimum of training to make them able to perform their function as bloodhounds and beaters, so it's doubtful they're given this level of insight.
Vader however (and the Grand Inquisitor, obviously) is perfectly capable of making his own and has had plenty of opportunity to claim a crystal from the weapons of fallen Jedi. Indeed, after the temple massacre they probably have quite the overstock (assuming they haven't been put to other uses.) Plus of course given how many times Anakin damaged or destroyed his previous sabres, he probably has more experience in it that anyone else in the order.
Anakin was certainly good at loosing his saber. The Quartermaster at the Temple was probably rolling his eyes every time Anakin came up for more components.
If I had to guess, I'd say Vader's crystal was claimed from Windu's saber. Presumably it fell onto the grounds of the Senate building a certainly wouldn't have been left lying around there for long. It also seems appropriate give that it belonged to the first person Vader killed (mythologically speaking.)
I could see that as a possibility, though it begs the question as to what made Mace's crystal purple. Also, why would Anakin choose that particular crystal? Anakin strikes me as the kind of person of forging his own connection with something unique, not accepting hand-me-downs.
You're asking for a logical answer to a mythical question. What are Mjolnir's criteria for "worthiness"? How does Excalibur know Arther was the true and rightful king?
This always amuses me-in real life I am expected to be skeptical of my religious upbringing. But, in a story I have to accept it?

If this is the answer, than "Red=bad" and Blue/green/purple=good" is just as valid.
The short answer here is that the crystals don't choose so much as the force guides the Jedi to their crystals. It may be as simple as the crystals best suited/more compatible for them, or something deeper. Destiny in an inherently circular concept. Also remember that the "impression of the crafter" doesn't prevent anyone else from using it, just provides the one that forged it with a deeper connection. It's a part of them.
Which was already pat of the lore.
So do you want more information, less, or all of it all the mysteries solved all at once? Having questions is a good thing, it means there's still some mystery left to uncover. Personally I prefer things to be revealed naturally and at the appropriate time. In the mean time, it's fun to speculate and try to puzzle it out oneself with the pieces at hand.
I don't mind asking questions. I love it, I love discussion, but I also get frustrated when I'm told "This is how it is-accept it." Well, it's a fictional world that I have engaged with since I was 8. I don't blindly accept anything now. So, yes, I have questions, and if I find answers lacking, then I'll question them further.
In the EU, it varied quite drastically how important or special lightsaber crystals were depending on the author. There was no set doctrine. Some said you could use almost anything, including common gemstones. Other said only adegan crystals would do. Others still said that the best kind were simply rare. Not intrinsically special, just higher quality. Very few made any kind of connection to the force. The weapon was simply a weapon. That force users built them was credited more to the delicate care and precision in aligning the focusing assemblies with the force than anything deeper.
With this new lore, constructing a saber isn't just a test of technical skill or scavenger hunting, but also one of spiritual insight. It doesn't complicate the matter, it adds depth and meaning.
Take the aforementioned line from Vader in RotJ:
"I see you have constructed a new lightsaber. Your skills are complete. Indeed you are powerful, as the Emperor has foreseen."
Now with the new lore this implicitly means
"you were able to seek out and forge a connection to the crystal, then assemble the blade unsupervised"
In the the old lore, this statement basically means
"hey, you can use a soldering iron and focus a beam! Good Job!"
I don't know about you, but I think the former is a much stronger qualification for the "indeed you are powerful..." part.
I think there is more to it than that, but I don't feel the need to argue the point further. Suffice to say, Luke's ability to construct a lightsaber was a an accomplishment in of itself, as the knowledge to make one would be limited, by design of the Emperor. The implication that Luke's ability to forge a connection with a crystal makes him more powerful is something I don't see.
That's from the micro series IIRC, so not in canon and thus could do with being restated in something that is. Again though, nothing here is being contradicted, only elaborated on.
Thank you. Couldn't remember.
The hilt is just refined metal and wires. A made thing. No more in tune with the force than a droid. The crystals are a product of nature and not to get all new-agey, but these particular ones seem to almost be alive in a sense. Though perhaps it's more accurate to say they resonate within the living force. Reflecting, focusing and amplifying rather than generating it as life does.
So yeah, it makes much more thematic sense for the crystal to be the key component and the source of a tangible connection to the force.
That's a point I had not considered, and certainly is an interesting facet to the construction. I'll grant that.
However, I'll still dispute that the crystal changing color in response to the contructor is unnecessary.
I'd like to hear how exactly does this complicate anything? Can you give examples? Honestly I just don't see it.
First of all, if the weapon is connected to the user, how do they keep losing their weapons? No, I'm not talking physics of combat or what have you, but why is a trope of them constantly losing it if they are connected to it in a way that is very unique?
I think this works with Luke who, in ROTJ, especially, he is able to call his saber to him even after discarding it or falling. In the PT, well, it's Anakin-need I say more?
Secondly, this is a small bit of lore that ends up putting way to much emphasis on the lightsaber and not on the Force. The Force is greater than the saber not the other way around. Now, I already see the counterargument that the saber color will reflect the fact that a Jedi was able to construct a saber and connect with the crystal in a meaningful way, which is then reflected in the color of the blade. But, why is a lightsaber the focus? Why not a connection with the Force?
As a follow up, I don't really have a solid example. I think that this bit of lore focuses too much on the saber, and adds to the mysticism in a way that is unnecessary. However, I am looking forward to your reply
ETA: Since I think on these things way, way, too much, I want to add a bit of clarification. My main objection is that the color of the crystal is changed during the construction process rather than the Jedi selecting the color or the Sith constructing the color crystal they want.
I don't think there is anything taken away from the lightsaber by keeping its connection to the constructor by the Force. However, I think the color change to the crystal is a curious addition, one that adds the question of why blue and green are reflected by the Jedi.