[84LX89GT]

I'm sorry to hear your car woes, it's never pleasant to have that many problems.
Did it sound like it was backfiring through the exhaust or through the intake?
There's alot of things that may cause a backfire/misfiring, so i'll list as many things as i can think of. unfortunately the only way to single things like this is out step by step diagnosis.

It sounds like no matter what your transmission is shot if it's actually slipping. Although when you have drivability problems that can cause erratic shifting, but your trans problems sound deeper than just shift scheduling.

Lean (intake) backfire:
The MAP sensor (manifold absolute pressure) can cause a lean misfire especially under load because all engine calculations are based off of that sensor and it measures air density, they can fail and read that you're at say for example 30,000 feet when you're at sea level, which air is thinner so you need less fuel - causing the engine to run lean. Some ford dealerships have a diagnostic tool called a SBDS that can test MAP sensors, or you can read the frequency being generated by the sensor by backprobing the connector and measuring with a multimeter. It should read around 159 Hertz around sea level.
Also if it's a lean misfire/backfire, fuel pressure is vital and if it drops under load and isn't able to supply the proper amount of fuel, this could be a result of a plugged fuel filter, bad fuel pump, bad fuel pressure regulator or kinked line.
Is the engine running hot at all? Excessive heat in the intake manifold/head can cause the air/fuel to light before it gets in the combustion chamber.

Rich (exhaust) backfire:
A backpressure sensor could be used to test if the catalytic converters are plugged. If the converter(s) are plugged it will kill power especially under high load and cause exhaust to push against outgoing exhaust eventually pushing it back in the cylinder/intake manifold when the intake overlap begins.
If you're engine is running really rich it will dump fuel into the catalytic converters and they will light there and can cause backfiring in the exhaust, and eventually melt the catalytic converters by super heating them.
To test for it running really rich a fuel pressure test is the first thing i'd do (it's one of the first tests that should be done since it's the least intrusive.) If fuel pressure is really high the processor will be unable to comprensate for the extra fuel by cutting back fuel trim and your car will run rich. High fuel pressure can be caused by a bad fuel pressure regulator or kinked return line.
Another test that can be done is block off the fuel return line and measure fuel pressure leak down to see if any of the injectors are stuck open dumping fuel.
Has your mechanic done any diagnostic scan tool tests to see what the processor is reading, diagnostic trouble codes help alot in determining the possible cause.
These are the biggest things i can think of and i hope it helps you out, good luck.