My first impression (pure speculation)..given it is a '92 and you have backfires and sluggish, plus high fuel burn...several 3.8 of this model year did not have a Exhaust Gaz recirculation valve and the settings used to meet EPA emission made it prone to burning exhaust valves....and this condition would indeed procure the symptoms as you describe.....
Now to verify this would require a compression test...and this is not very easy given the way the engine is squeezed in, but because this has been reported in the past, it would be wise to confirm or eliminate this option before going for something else. check for this part:

If you do have this EGR valve, then this speculation is much less of a possibility.
IN the mean time, do you have the CHeck Engine LIght ON?..in which case it would be easy to pull the codes, just in case it would lead to something.
www.avigex.ca/xport/readingcodes.jpg
(bottom line: connect A and B, turn key ON, count CEL flashes.

ALso..just for a test, disconnect the MAF sensor; in several cases with a faulty MAF, disconnecting it forces the computer to default mode..and it then runs better than with a faulty MAF, although it is not optimised.
Faulty TPS might cause some erratic behaviout also, but would not be as dramatic....anyway, the last two conditions should light up the CEL.
Other possibilities : faulty O2 sensor: this would procure normal starting..but as soon as warm, when ECM turns to closed loop operation, faulty O2 signal would mess up everything...
ANother classic: Crank Piosition Sensor..but the symptoms are different....no start, or starts..then stops at next red lignt...
Best would be to have a few CEL codes....