Ah...
Not much to "compensating", of course, for the most part... as you rarely if ever get the compensation node brought out to a pin. Which is part of the reason why they're so notoriously finicky (when they do behave badly, there's simply nothing you can do about it).
I prefer switching regulators with external compensation, for the same reason.
Alas, because the average engineer is happy enough following a "typical application" and doesn't want or need to deal with compensation each and every time, the value of internal compensation is real. So, it's not going to be going away any time soon.
As for testing, I normally do a step response test, which can be as simple as scoping the output rail and 'sparking' a load resistor across the output. Ideally, the same should be done on the input side (source step response / PSRR) as well, and also over the expected range of input voltage and load current, in case it varies with operating condition (which it often does).
Without access to the error amp, loop response isn't really a thing, but you could test PSRR and Zo vs. F, which is basically to the same end. The step response is more limited (it doesn't provide exact data at any given frequency), but arguably may be more informative (a true large signal test).
Tim