Back pedal woes

The correct answer is, don't use big-big, it overly stresses the chain and increases wear on the chainrings and cassette. You should make a habit of dropping into the small ring about 4-5 cogs from the lowest on the cassette.

That said:

1. have you checked the rear mech hanger alignment? You say you changed it, but even a new one can be improperly aligned.

2. Did you change the front mech height after fitting the compact cranks? it should be 2-3mm above the chainring teeth.

3. If you're using big-big a lot, you may have worn the angles of the chainring teeth so that it's allowing the chain to drop in reverse.

4. Did you shorten the chain when you put on the smaller cranks? Incorrect chain tension can cause all sorts of problems with chain drop.

5. Pedal forwards not backwards. The freewheel is there so the wheel can go round when you stop pedalling, not so you can pedal backwards ;))

I can't say I'm much surprised - pedalling forward, the front mech keeps the chain in place.  Pedalling backwards, there's nothing to stop the chain dropping off the big ring if it's minded to,  and the rear mech will be pulling the chain over to the inside.  Maybe the chain is now too long if you didn't take some links out, although not sure that that would help

I'd expect a front mech to be barely free of the inside of the chain big-big - indeed without trimming (and SRAM often don't do trimming) it can be hard to avoid rubbing and get a clean change, so it should actually be hard to drop a chain. Check derailleur is parallel - it may be tempting to set an angle to get the front closer to get the pressure for the change while having the rear "loose" to avoid cross-chaining rubbing. As SRAM don't give you a second bite of the cherry when changing the front derailleur (anyone else a second click of the shifter can increase the changer pressure, SRAM releases then gives you the same shift again) so with SRAM it is often a game to get the derailleur set correctly if even possible. A few years ago I would always substitute a Shimano front derailleur rather than spend time trying to get a SRAM one to work - it was cheaper (depending how you value labour).

My first port of call would be to check the front derailleur is at spec. height above the teeth given that you've changed the derailleur position for the change from 53 to 50.

Next question would be: what state is the freehub? A sticky freehub will tend to resist back-pedalling and you would see the top chain go very slack, dropping down on or below the chain stay when coasting or back-pedalling.

Final point, resist back pedalling - if you are coasting and swapping which pedal is down for a corner, pedal forwards. Aside from setting pedals for starting off, I don't think there is a good reason for back-pedalling. You'll soon find that winding the crack backwards with the bike in the stand that chains don't run properly backwards on any bike except when the gears are closely aligned.

Does contact between the chain and the front derailleur actually ship the chain into the small ring, or does the chain simply fall down "on its own" (due to pressure exerted on the chain by the extreme chainline)

Some race frames don't support compact chainsets, needing a minimum 52T big ring

It's most likely to be a chainline thing, have you installed any required spacers correctly, and torqued the BB shells to spec? (No idea about SRAM BBs and whether they use spacers)

I had one frame which did this, never solved it, but didn't consider it an issue because I didn't back pedal in big-big.

To be frank/cheeky, the problem is probably the fact it's a SRAM front mech, there's a reason why they advocate 1x drivetrains. I can't remember, do they have trim settings which move the front mech cage away from the chain in cross-chaining situations?

This is a problem? I guess try adjusting the H limit screw on the front derailleur if it is touching the chain in big-big. Make sure it can't touch the right crank, though.

Or just don't use big-big. Or don't back-pedal if you do.