stall on deceleration

Been wrenching on this thing awhile now(fe550e, 2004)..carb cleaned( WELL),cam timing set, valve clearance set, throttle position sensor(plugged/unplugged), tried higher idle, fiddled with slow mix screw.....still stalling on hard back shifting. Not every time but maybe one out of five. It will fire right up, once I find neutral. Pull hot start button,very slight opening throttle. It will start without the gas just takes another turn on the crank to light up..runs strong I don't have anything to compare it to, has been awhile since I've had the xr600r running. I'm a streetbike guy(DOHC inline fours). The only other thing I can add is.. it pops a bit downshifting not much more than my hot rodded zx11 track bike.
Thanks for everybody's help.
I really dig this bike! Starting to see see why y'all love these things..handles like a 250 ....hits like my street bikes

Okay I will dig around the forums to find a tried and true combo as a baseline and start from there. I also forgot to mention when the carb was out I pulled the throttle and a long squirt went across the garage. This was more fuel I have ever seen from a motorcycle. Is this normal? Does this bike need an accelerator pump? I ran across a few folks here with 650s say they disabled theirs
The previous owner says he never had this stalling issue. He bought a VOR and this sat for a few years. So it needed the typical used bike stuff

Ok, ill check the manual for the closed course setup after i try opening the mix screw(i only went to 2&3/4 out). The bike dosent have the hour meter installed it was in the spares box, so i dont know the hours. But the P.O. said he didnt ride it much. He has a pretty big stable mostly vintage stuff. The stuff he has is eye candy the Berg and a Husky looked like the only ones he rode a bit. Anyway it could have a bunch of time on it but you couldnt tell by looking at it. Good idea i hadn't considered doing a leak down on it. I should have done that already. Thanks ned and husabutt!

Can someone translate for me? I don't speak Taffy too good!

Some observations from riding yesterday....
Cold start..a/f screw 2.5 turns, choked...started,not right up but ok
After stalling..@ 2.5, hot button out....would not start
@1.5, hot button out....fired right up, high idle
Hot button in....idle normal, lean popping
After starting turn to 2.5, (idle dropped a bunch
Increased idle= popping almost gone
Stalling problem persists. Could putt around all I wanted. As soon as I cranked it up ..thrid gear, fourth gear pinned..downshift heavy engine braking. It would start sputtering (like running out of fuel) and never recover. restarting.see above
Checked float..pain in the ***..all good, float level with base

I've given myself one more week to sort this bike out before it gets relegated to the back of the garage. To make room for a more viable motorcycle. One that I can concentrate on riding. This bike needs an owner that enjoys a challenge that doesn't include riding.
Ill do a leak down and pull the rocker box to check springs. If I don't find something ill have to buy the KLX I should have bought in the first place.
I think the jetting is close..but...
I don't understand the high idle on hot start
2.5 turns on screw(to stop lean popping), slows idle..This confuses me.
It should come up as it reaches the optimum
The stalling is "THE" problem.
The only thing not checked that makes sense to me is the broken exhaust valve spring acting as a massive vacuum leak

Anything else I should look for? Before it is time to punt

I pulled the carb out again reset the float past spec.(more fuel in the bowl)
Cleaned everything up backed off the squirt, ckecked the new plug=dark and sooty...adjusted valve clearance..backed off decompression cable to make sure it wasnt partially engaging..same result under hard engine braking it dies. It feels like it ran out of fuel. It will start up only after it comes to a complete stop. Talked to the previous owner again, he only used it for trail riding, mostly just second and third gear so he never experienced a stalling problem. I have to find another bike that i can ride for now. I will come back to the Husaberg soon and try to sort it out. If anybody runs across a similar problem any solutions would be appreciated. Thanks for everybody's help sorting out water pump seal/left case/kickstart problems