2004 suzuki volusia engine quits while running

2004 Suzuki Volusia 40k miles ridden near daily. Starts and runs but increasingly quits while running. Either at an idle in the garage or at speed while riding around. It begins to run rough then completely quits. Backing off the throttle while riding will allow it to recover then throttle back up to previous speed - it dies again. During the dying backfires/flames out the exhaust. Back off the throttle engine catches again and will run. When it first appeared it only happened at 70mph or higher. The speed it occurs at has been slowly decreasing where it can now be reproduced at 55-60mph. The last time it happened I was down to 40mph before I could get it to recover. It also will just quit if sitting at an idle for 15 minutes or so. My brother is fairly competent at maintenance and has done his own on everything he owns for years and this has him stumped. What's been done (not in this order just trying to remember it all): -this bike had stock pipes debaffled (back plate and baffle removed f