Your description entails the probability of TWO simultaneous problems, one 'started by the other': • backfire due to sticky exhaust valve(s) and • 'rotting' exhaust manifold.
The more serious and more common problem is the rotting exhaust manifold ... which carries the potential of water leakage into a cylinder.
Universal exhaust manifolds for the A4 are notorious for the development of internal slab rust in the water side. These large platelets of 1/16 - 1/8" thick of 'nickle and dime' sized (red) slab rust are formed when the cast iron begins to 'stratify' and the growing (red) rust due to its low density begins to 'push' the manifold casting apart (on the inside). When these platelets break loose they drop to the bottom of the water passages, the A4 manifold has its water inlet/outlet on top so the slabs remain inside the manifold ...... UNTIL there is a hydro-shock such as an engine backfire that 'reverse' enters the water outlet/injection nozzle of the A4 'steam riser', etc. and which causes the platelets to become 'entrained' in the water flow, temporarily block the water exit nozzle, are held in place there until the engine is shut down, then to fall back down to the bottom, .... usually.
That the manifold is now probably 'slab rusting', there is a high potential that there is also a 'pin hole' between the water side and the gas side of the manifold. When an engine with a manifold with a pin hole is shut down, as the engine cools it is capable of drawing water into the combustion chamber .... the first sign is 'sticky valves' (occasional 'backfires') or sudden loss of compression in one cylinder.
The cause of slab rust is greatly accelerated by 'drying out' the engine for long term storage (slab rust is also formed inside the engine block - its the principal cause of 'end of life' of an A4 - 'rot'. The protection is to 'run the hell' out of the A4 (or any other cast iron engine) so that instead of destructive red (ferric) rust is formed, protective 'black' (ferrous) rust is formed. Heat soaking the engine at above 160-180+° for long periods will promote the conversion of red rust to black rust; but, black rust will slowly change back to red rust, so you have to 'run the hell out such engines'; plus, when long term storing you 'should' keep all the water passages filled with antifreeze that contains anti-rust compounds. Slab rust is why the USNavy will 'never' shut down a cast iron engine, unless absolutely necessary .... constant running prevents the development of 'red' rust and especially 'slab rust'.
- remove the exhaust manifold, push a stiff wire into both the inlet/exit and break up the slabs as best as possible, invert it and shake them out. Put a water supply/hose with a gage and water tight valve on either the inlet or outlet, block off the other; apply pressure (~30 psi) then shut the valve and watch the gage. If the pressure slowly drops or you see water coming out of gas port = Pin hole !!!!! (and you also found the reason for the sticky valve(s)).
DO NOT, unless absolutely necessary, 'acid treat' a manifold that has developed 'slab rust' as you will greatly accelerate the slab rusting. If you MUST acid treat due to carbonate build up, ONLY use an 'inhibited' commercial boiler descaler such as RydLyme and then (always) follow up with the 'pressure leak down' test - RYDLYME Marine: The Ultimate Biodegradable Marine Descaler! | RydLyme Marine
Sticky valves - spray PBBlaster onto the valve stems and let soak. If 'stuck', bend a long screwdriver into a 90° shape, go into a sparkplug hole and PUSH the offending stuck valve down, spraying the valve stem with PBBlaster. Hand rotate the engine a few times to insure that the offending valve is 'free'.
Obviously such manifolds are obsolete and long out of production. Rumor has it that Moyer Marine, Cambridge Maryland moyermarine.com has a casting source for the manifolds (and the engine blocks).
Never ever 'drain the water' from such an engine for winter or long term storage, always fill both the engine and manifold with antifreeze with anti-rust compounds.
RUN THE HELL out of these engines so that they become HOT for long periods, so that the rust that forms inside is protective BLACK rust, and/or that you change the destructive red rust back to black rust .... and do so 'often'. I think its better to run an A4 with a 180° T'stat and suffer having to regularly 'descale' (with 'inhibited' descaling compounds) than to buy a new manifold (or a new block); the alternative is fresh water cooling with a heat exchanger (with the manifold in the FW loop). I make this FWC recommendation even if youre running in fresh water as the FWC circuit will automatically 'deoxgenate' the water; hence little to NO internal rust. Constant oxygenated fresh raw water from a lake or river will cause internal 'rust'.
Other: If your A4 discharges its exhaust into a vertical copper 'steam riser', consider to cut the riser apart and check to be SURE that the deflector plate (witches hat) is still in place .... if it isnt the injection water will discharge directly into the exhaust pipe and ultimately back into the combustion chambers of the engine. The old steam risers are 'the best', and its best to repair them if needed.
Steam riser with 'witches hat':
hope this helps