Deso would fit most of your criteria, except it's 5 days & no class IV. May-June would be a good time to go, but there would be mosquitos at that time. Permit required.
San Juan from Sand Island to Mexican Hat, or Mexican Hat to Clay Hills. Great scenery, hikes, good weather in May-June. Class II/III. Permit required.
Another, milder option would be Southfork Snake. Conant to Byington. Class II, nice camping, fishing, bird watching. Definitely a laid back 3 day float possibility. Pretty tame stuff, but you could stop for a day run on Alpine Canyon for your class III-IV fix depending on weather & flow. Self permit at Conant.