Yes, you can swap in a 3400 LA1 where an LH0 (your 3.1 MPFI) resides. From my understanding, the 3400 is a bored out version of a 3100 (L82), itself an updated LH0 with SFI and other minor improvements. Your real issue will be that you may have to convert to OBD2 or send your computer out to WOT Tech or Milzy Motorsports to get the computer programmed to run the LA1. That would eliminate the probability of issues with the new engine.
What most guys have done here however is swapped out the 60 Degree V6 (the 2.8, 3.1, 3.4, 3100, 3400, 3500 engine family) for a Buick 3800 S2. You could go supercharged or keep it naturally aspirated, however this would be the easiest thing to do as the 1996 Buick Regal and 1998/1999 Chevy Monte Carlo both had a 3800, but in naturally aspirated form. In theory, you could get a donor 96 Regal and convert your 93 to OBD2, and 3800 power it along with the transmission since the 3.1/3100 had the lowest gear ratio of the 3 engines available. The LQ1 had the highest ratio at 3.42 and I think the 3.1 had it at 3.30 or something along those lines.
There's a lot of threads of people swapping a 3800 in their 1st gen cars on here.