Power mixture set too lean... LPG tuning guide
The problem is that the power mixture screw/bolt (the one that goes from your gas converter to your throttle body) is set too lean (screwed IN too far).
I had the same thing on my VQ, a couple of times i was lucky and it just blew off the overflow hose going from the LPG to the air box and just made it so the car would stall at idle on LPG. Another time i was UNLUCKY, and it blew apart the top half of my air box... the car only worked on petrol until i got it replaced.
You basically just need to re-tune your power mixture screw... you need to find the right balance between being so lean that your car backfires at high throttle from the INTAKE (not the exhaust), like it sounds like it's doing, and being so rich that you get really poor economy...
Another way to tell if it's set too rich, is that the car may seem like it's being more powerful, and more responsive, until you put your foot past 2/3 and it doesn't go any faster. It you set it way too rich, and were really lucky, you might get a backfire out the exaust (which would be quite cool) but i've never seen it happen, and i don't think it could unless you deliberably unscrewed the power mixture screw all the way... anyway, if in doubt, set it more rich than lean, you may get crap economy, but at least you won't blow up your airbox!
In your case, I would start by turning the screw out (anti-clockwise) about 3/4 of a turn... if you notice it starts getting crap economy, screw it in 1/8 to 1/4 or a turn at a time, until you get the right balance. You'll notice when it starts getting too lean, because just before it gets to the stage where it risks backfiring at high throttle you'll see a noticeable decrease in power. If you turn it back rich again just past this point where you get the extra power then your LPG tuning will be perfect (for 6 months or so).
If the car happens to have any trouble idling on gas, the power mixture has nothing to do with that. That's controlled by a much smaller bolt (the idle mixture screw) which is most proberbly on your gas converter near the pipe that has the power mixtire screw on it... on an older carby car i had, the idle mixture screw was on the mixer, on top of the air filter, but on gas for EFI systems i think the idle mixture screw is usually on the converter. If you do need to play with it, you just set it to where the car will idle most cumfortably without stalling.
Oh, the kitty flap is also a good idea... personally, i've tried putting a hole in it, then covering the hole with gaffer tape from the OUTSIDE. That way, if it does explode in the inlet pipe, it will hopefully just blow off the gaffer tape, rather than blowing apart your airbox. Obviously though, avoiding these backfires in the first place is the best way to go.
Hope this helps :-D