If you aren't looking for a class V experience (which SFS in May will be) you might consider the Jarbidge Bruneau.
Other venues for very long floats in May would be:
MF Salmon to Riggins (or heller bar)
NF John Day to Cottonwood (couple dams above service creek, dunno the sitch on that) Service creek to cottonwood is 130-odd miles by itself with great hiking.
Minam into Grande Rande. fly into Red's Horse ranch, go all the way to Heller Bar
Deschutes -- a quick car assisted portage of Shearar's falls and you can link up the upper and lower des chutes. The town of Minam surely has someone who'd meet you with a trailer to assist in that portage.
SF Salmon is very hard, consequential class V. I've done it only a between 1.8 feet and 2.4 feet in IKs. Had friends lose limbs and see god at 9'. Can't emphasize enough that in snowmelt temps and high flows, this is an Illinois at 4,000 cfs V-V+ with serious consequences kind of trip. Only folks with rescue experience and solid self-rescue skills should consider the SF in May. Maybe that's your group in which case, have fun and be safe.
Folks looking for a IV+ experience on the SF should go run it in the low 2' range, which it will often hold into late July. No one there when it's low, and you get those white sand beaches all to your lonesome. One of my favs.