It also reminds me of the second pilot, WNMHGB. The warp drive is knocked out due to trying to cross this galactic barrier, and this is one of the very few times Trek successfully sells the notion of being truly trapped out there and it's palpable. A ship losing its ability to travel faster than light is now stuck and with limited resources and confined in scope to keep the audience focused. A great blend of the fantasy and the reality where nothing trips over each other to pull one out of the story. It's great stuff.
Except they're conveniently within a few days' sublight travel of a habitable planet, which would have to mean they came out in its star system already, and why would there be an Earth refueling station that close to the edge of the galaxy if they'd never been there before? I don't see anything realistic in that situation.
But you're right about the early seasons of TNG being as scientifically grounded as Trek has ever gotten, thanks to Rick Sternbach & Michael Okuda as science consultants. The depiction of a periodic nova star in "Evolution" was so accurate you could use it in a classroom. The time warp in "Yesterday's Enterprise" was caused by "a Kerr loop of superstring material," which, aside from misusing "superstring" to mean "cosmic string," is an actually plausible mechanism for a time warp, certainly more so than chroniton fields or what-have-you. (The word "chroniton," whose only use in TNG was in season 5's "The Next Phase," doesn't even make etymological sense. The proper construction for the name of a time quantum would be “chronon,” but that's already used to refer to the smallest possible interval of time in a quantum system. The Greek root for time is khronos, and the suffix for a subatomic particle is simply -on. If it had been “chronicon,” that would make sense, since khronikos means “of/pertaining to time.” But there’s no inflection or declension of khronos that has an “it” in it as far as I can tell.)