Yay! I woke up to so much feedback and ideas a mere 7 hours after posting. I love the semi-collaborative nature this thread provides me.
1)
The laundry "chute". My apologies, guys. I didn't mean for it to be a literal "chute", with a complex conveyance system made up of tubes inter-crossing decks, as I don't like that idea at all (I remember reading once or twice an explanation that food was delivered to the "food slots" onboard the TOS-E via a system of mini-turbolifts and thought that idea was atrocious). I meant the "chute" to be a place to deposit one's laundry, where it would then be beamed to the laundry processing center somewhere on the ship. I dunno how we feel about widespread intraship beaming in the TOS era either, since "Day of the Dove" establishes intra-ship beaming to be quite dangerous or little-tested during the TOS era. However, that was an instance without transporter machinery on the other end (Engineering) so maybe it's considered safe as long as a receiving-end transporter is being used.
However, I do like the idea of a small "future washing machine" of sorts instead of a "laundry chute", where clothes are placed inside and then are dematerialized/cleaned/rematerialized, as TMoST indicates as
@feek61 noted above.
2)
The shower. For the block-in, it's currently the same diameter as the sonic shower we see Ilia getting out of in TMP. And yes,
@lawman, the half-cylinder you see here is just the exterior of the shower, but once modeled will be a full-cylinder inside. I may adjust the diameter of the shower unit to allow for more room once I get to modeling and seeing how well a human body would fit inside.
As of now, I’m leaning towards making it’s a hydro/sonic hybrid (implying this with a shower head and a control panel interface with an option labeled “sonic”). Also, aesthetic-wise, I’m imagining it with a radially rotating frosted glass door and it lit with a colorful TOS hue from inside.
3)
Layout. @Lt. Washburn makes an interesting suggestion regarding maximizing space by moving the sink/mirror combo to the wall opposite of the commode to allow for an open-closet area to area beside the door. I'm in favor of exploring this idea, but my main concern is that moving the sink to the wall opposite of the toilet will greatly cramp that section of the bathroom, and I really can't extend the width of the bathroom anymore than the 6 feet I've already allotted. I will experiment this evening and see how the space feels with the sink moved to that wall.
4)
Food Processor. Unrelated to the bathroom, but
@Mytran brings up that we only see an in-cabin food processor in use in the Mirror Universe version of Kirk's cabin, and that use is theoretically restricted to beverages. While this is true, we do see that the food processor remains in subsequent Prime Universe appearances of the cabin. We never see it in use, but it is still unmistakably a food processor. Here are the examples:
In Kirk's cabin:
In Spock's cabin:
In Uhura's cabin:
In the guest quarters:
I've included it in my build as well, but thought that maybe it's only for VIP guests and senior officers. We see in "Obsession", Lt. Garrovick, a junior officer, does not get a safe in his quarters like the senior officers do, as they covered up the safe with a plain panel, This leads me to believe that a similar panel covers the area where a food processor would be installed on the other side.

This also leads me to believe that if the producers/set designers of TOS didn't want a food processor to be present in the accommodations of Prime Universe senior officers, they would've covered the food processor with a panel in the several instances we see one, much like they did with Garrovick's safe.
Whether the food processor present in senior officer's quarters is limited to only beverages or light snacks rather than full meals is another topic of debate. Thoughts?