PVLIR seems likely if it was your first time to remove the tank.

(petcock vacuum line doesn't go where it looks like it goes.. it actually goes on the back of the petcock pointing to the right, and not the bottom)

 

That would be my guess also.....

 

All hoses are hooked up correctly. As I understand it, backfiring usually occurs from lean conditions. Is that right? Can the jet needle be moved to a different position? I removed the slide but it didn't look like the needle was adjustable.

 

Well if you removed the slide, you did a lot more that what you told us and that leaves a lot of other things you could have done wrong. The first thing to check is to see if you reinstalled the diaphragm(s) correctly. You need to lift the slide and see if it just slams closed or does it drop slowly. If it just slams shut and you don't here it pulling air in, the diaphragm is not seated correctly. Then you need to check all the hoses on the bottom of the air box.

To answer you question though, the stock needles are not adjustable unless to shim them. The fact that the bike didn't backfire before you pulled it apart points to something you did.

 

The old plugs look just a bit oil fouled. If it had been running lean, I should be seeing carbon deposits. Right? I'll lift the tank and check all hoses for kinks.

 

The diaphragm is seated and sealed well. I lifted the tank to check all hoses for kinks. None that I can tell but it's not backfiring under acceleration now so maybe there was. But it still does it a little when I let off the gas. Is this normal being a V-Twin?

By the way, I'm new to the forum and have noticed a lot of military men are members. Thank you for your service. God bless you all.

 

If the pair system is still hooked up it will do that on deceleration.