OK,
Before you "throw parts at it" take a diagnostic approach.
First,
A bind up in the forward clutch drum will cause a no reverse condition BUT at the same time you will have forward drive in neutral, as if in 1st gear.
Reverse will act like a transbrake, the engine will load against the stall converter, the vehicle may engage reverse and drive through the welded together or too tight forward clutches.
You need several things for reverse to function.
First you need pressure.
You have this if it drives fine in forward gears. Don't mess with the pump or converter, they are proven good if you have forward gears.
Second you need drive from the engine. You have this, the converter is working in forward gears, so it's fine in reverse as well.
Now,
you have two major elements that need to hold for reverse internally.
The Low/Reverse band and the Direct (3rd) gear clutches.
As Crosley stated, an air check on both of these is easy.
Check both sides of the center support bolt. One will hold, the other will leak out the opposite hole but also apply the clutches.
Go ahead and check the center support bolt itself, this is 2nd gear.
Now the hole at the rear of the case goes into the servo. Air check it but put a rag over the servo area, because you are going to get lots of ATF from the backside of the servo.
If all air checks good, you may have a too short servo pin. This has become an issue on the TH400's and 4L80E's in recent years IMO.
Band diameters must not be held to the tolerances they used to. Band clearance must be closely checked on the TH400 and 4L80E.
Take a good OEm band out, install a new OEM band, and put it together and in some cases the damn thing won't have reverse.
The only plausible explanation is the band diameter or overall length has changed.
If you have 3rd gear, look at the band and servo area closely.
90% chance this one can be fixed in the car...