Overheating Linear Voltage Regulator In Lexicon Omega Audio Interface. Can I Swap With Reduced Amperage To Avoid Heat Probs?
Is it crazy of me to think the 7912CV (-12V, 1.5A) could just be swapped for the 1.0A version of that one?
Something like an ON MC7912CTGOS-ND which is -12V at 1.0A?

You're misunderstanding the current rating of a voltage regulator.  It is physically impossible for a two-terminal source to control both the voltage and current at the same time -- the load pulls a current that's a function of the voltage that it sees (or it develops a voltage across its terminals that's a function of the current you shove into it).
If the load pulls 0.75A at 12V, then it's going to pull that same 0.75A at that voltage whether the regulator is rated at 1.0A or 1.5A or 150A.
The LM7912 is a voltage regulator.  That means, it regulates voltage.  As stated above, that means that it holds the same voltage no matter what the current draw is -- up to the point where things go sideways.
The voltage rating is what it does.  The current rating (1A or 1.5A) is what it can stand.  If you put in a lower-rated part in there, it'll probably just overheat quicker.
If it takes a couple of hours of continual use to have a problem, then it's almost certainly a problem with getting heat out of the case.  Normally I'd recommend that you put a fan in there, but it looks like it's a pro audio part -- so I'm going to suggest that you find a small, really quiet fan, and put it in there, and my apologies if it's just too noisy for whatever you're doing.
Or, if there's no holes in the case now, you may be able to make it into a happy camper by drilling holes in the top &amp; bottom so that air can flow up the heat sink (and make sure the heat sink fins are vertical).