If youve got an offroad xpipe,the smog pump and every other thermactor system component can be removed completely because those components are serving absolutely no purpose now that the converters are gone.Codes will likely be present afterwards,but those codes will not cause any driveability issues,as long as the system was deleted properly (i.e. - you plugged the vacuum hoses,capped the xpipe airtube,etc) Any codes related to the removal of those components are called "soft codes" and they harmlessly stay dormant in the ECU.Their only purpose is to help you repair the thermactor system back to original factory specs,if you were ever to add converters again and needed the thermactor system intact.
I can see how your theory of leaking check valves could be a possible cause of the backfiring,but Im not sure just how possible?? You mentioned removing the vacuum hoses from the smog pump,but I believe you meant to say (& Im assuming of course) that you removed the vacuum hoses from the tab & tad valves?? If my assumption is correct,removing those hoses would trigger the following
** When the vacuum source is removed from the bypass valve,it triggers the valve to dump any air flowing through it out of its silencer ports,which dumps the air to atmosphere. **
** When the vacuum source is removed from the diverter valve,it triggers the valve to dump any air flowing through it out of the port thats connected to the xpipe airtube hose,which dumps the air to the xpipe.**
So with that said,I wonder if outside air is being drawn into the bypass valve,via its silencer ports since they're always open now with the vacuum source removed, then making its way thru the diverter valve & on to the xpipe,where its likely creating a lean condition and subsequent backfiring??
Another possibility could be if unburned fuel is reaching the exhaust where its igniting and causing backfiring.Then once you reconnect the smog pump and its air reaches the exhaust,its leaning it just enough to compensate for the unburned fuel and this is removing any backfires.
If you remove the diverter valve hoses from the crossover pipe and the xpipe airtube,then cap both pipes and the backfiring disappears,your theory about the check valves may be spot on.
I should've asked in the first place,but this backfiring is in the exhaust,right,and not in the intake??
If code 44 popped up with the smog pump/thermactor system functioning, that code usually means the crossover pipe and/or the thermactor passage on the passenger side of the pipe or head is clogged with carbon buildup.The carbon will be so hard you'll have to use a chisel,
dremel tool,etc to clear the pipe or head passage.That condition would normally send more smog pump air to the driver side passage,causing a o2 sensor lean code on the driver side,but since your problem is only occurring when the smog pump is bypassed,a clogged pipe/head passage would have no bearing on the backfiring condition.If it was the other way around & the backfiring was occurring with the smog pump running,then a clogged pipe could be the cause.