The only example on that TVTropes page allegedly from TOS that I see is from The Naked Time,
only they got it wrong there. In fact, in that case, Spock figured out how to shorten the time, not Scotty, and Scotty's estimate on how long it would take to restart the engines was for real, for all he knew. Spock knew something Scotty didn't. So, sorry, it's you who have failed to provide any examples in TOS.
The TWOK example is deliberate code, so that doesn't count. The STV example lampoons the trope, but without Scotty having inflated his estimate.
For shits and giggles here's the scene from Relics,
according to http://www.chakoteya.net/NextGen/230.htm
LAFORGE: Adjust the frequency stabilisation on the main deflector dish. It's out of synch with the aft sensors.
SCOTT: Laddie, you need to phase-lock the warp fields within three percent or they'll become unstable.
SCOTT: Well look here. The warp field is
(the computer rejects his commands)
LAFORGE: We use a multiphase auto-containment field now. It's meant to operate above three percent.
SCOTT: Oh. Well, that would make the difference.
BARTEL: We can re start the engines in ten minutes, Commander.
LAFORGE: Thank you, Lieutenant.
SCOTT: I remember a time when the old Enterprise was spiralling in toward Psi two thousand.
LAFORGE: Thank you.
SCOTT: The Captain wanted to try a cold start of the warp engines. I told him that without a proper phase lock it would take at least thirty minutes You canna change the laws of physics, I told him, but he wouldn't believe me, so I had to come up with a new engine start-up routine. Do you know that your dilithium crystals are going to fracture?
[As I said, it was Spock, not Scotty, in The Naked Time,
who figured out how to restart the engines faster. Scotty and Spock worked together to do it faster than Scotty would have known how to do it on his own. For whatever reason, Scotty kinda leaves that part out here.]
LAFORGE: We recomposite the crystals while they're still inside the articulation frame. Look, Mister Scott, I'd love to explain everything to you, but the Captain wants this spectrographic analysis done by thirteen hundred hours.
SCOTT: Do you mind a little advice? Starfleet captains are like children. They want everything right now and they want it their way, but the secret is to give them only what they need, not what they want.
LAFORGE: Yeah, well I told the Captain I'd have this analysis done in an hour.
SCOTT: How long will it really take?
LAFORGE: An hour.
SCOTT: You didn't tell him how long it would really take, did you?
LAFORGE: Of course I did.
SCOTT: Oh, laddie, you've got a lot to learn if you want people to think of you as a miracle worker. Now listen
LAFORGE: Captain Scott. I've tried to be patient, I've tried to be polite. But I've got a job to do here, and quite frankly, you're in the way.
SCOTT: I was driving starships while your great-grandfather was still in diapers. I'd think you'd be a little grateful for a some help. I'll leave ye to work, Mister La Forge.
Point to me where Scotty advises La Forge to pad his time estimates. While Scotty's evidently surprised that La Forge hasn't learned to gauge when the captain needs something right away or whether it can wait, we never get to hear what Scotty's actual advice to La Forge is, because he cuts Scotty off.
It seems to me that the whole point here is to make sure that the captain knows not to cut the margins so close that nothing can save the ship. Scotty's trying to keep estimates conservative to protect the ship, not his reputation. It was couched in humor.
And anyway, Scotty never did this in TOS anyway, not that I know of. I'm eager to see whether anyone can produce an actual example.