Thanks to people like you, a haynes manual and being a cheapskate I've been able to do all the maintenance and repair on my 85 K100 myself and haven't yet needed a mechanic. But this one's so complex its hard to know where to start. During a long trip I had several backfires when slowing down. Ran rough intermittently, now continuously. Pulled and cleaned/regapped fairly new plugs (all 4 black and sooty/running rich), checked wires and coils (all good) and battery is fully charged. Inspected all hoses, okay. Fuel is good as several other bikes filled from same pump with no troubles. Fuel filter is also fairly new and air filter is clean and properly seated. Any idea where to start? Bike has 52k miles. Thanks for any help.

Black spark plugs = too much gas or not enough air.

A bad setup or defective idle switch could create this problem. If the switch doesn't signal to the EFI computer that you throttle is shut off, the efi will continue to feed gas to the cylinders. Most of the time this is the problem when the engine back fire when slowing down

You should first recheck the air filter. If everything looks OK,you should check the fuel pressure. You may have a problem with the fuel pressure regulator and get more than 23psi pressure. If it's the case, your gas consumption should increase.

It's unlikely that you have 4 injectors failing at the same time.

Don't have access to a fuel pressure gauge at the moment. Did, however, notice the tps was out of wack. Adjusted it so you here the click just before the throttle is totally off. Runs a bit better, but I'm hearing a tap noise from somewhere around the airbox. Sounds kind of like a butterfly valve snapping open/close. Engine seems to miss when this happens.

Could it be a broken spring on the vane of the airbox?
If you check the air box, when you push on the vane, it should close freely.

the vane closes freely.