Thats an ambitious plan!....The Current is floatable year round from Baptist Camp on down..., but usually pretty skinny water till you get down to Welch Spring...plus there is that darn low water bridge at Cedargrove to portage...
I havent been below Round Spring in several years... but there are plenty of outfitters to run shuttles for you...
On the Upper Current..Best fishing is between Montauk State Park and Cedargrove...lots of big brown trout, some rainbows & smallmouth (Blue Ribbon regulations apply)...Cedar to Akers can be good if you want to bait fish for trout or eat some, some fair smallmouth and pickeral fishing too (White Ribbon Regulations apply). Akers to Pulltite just plain sucks for fishing but its a great float...paddle into Cave Spring...Fishing picks up at Pulltite...and Pulltite Spring is a must see...Pulltite to Round...Little Gem Cave is a fun detour.....Round Spring down if you want better smallmouth fishing
Jadwin Canoe does the Baptist to Cedar Stretch but they are located off the river aways and you camp in a field if you stay there. Montauk State Park, Ozark Mountain Ranch, and Eagles Park would be better camping options for the Blue Ribbon Area......Next outfitter served access is Cedargrove..no outfitter there, but plenty of camping...next Access is Akers Ferry...think there are group sites available there..plus Akers Ferry canoe rental& store they usually put in at Cedargrove, but you could probably talk em into Baptist for more money (Shuttles arent cheap down there... $54 for a car spot last time)...Next Access is Pulltite, big CG, Current River Canoe Rental & Store...Next Access is Round Spring...big CG, Carr's Canoe rental, store. I'm sure that someone else can provide some info on the lower river.
The Jack's Fork....May is a great time to float that...Prong's to Rymers is a favorite but it gets too low to float sometimes...lots of big rocks to watch out for on that float....I only use two outfitters down there...Harvey's Alley Spring Canoe Rental...and Windy's in Eminence...I havent been below Eminence in years either...someone else can give you the scoop on that stretch. Good smallmouth fishing over the entire stretch...(1>18" limit on a good portion of it too).
I'd probably do a couple days on each if you have the time and camp on the river....Primitive camping away from the access points in the boundaries of the Ozark National Scenic Riverways river is free and there are plenty of nice gravel bars to camp on. Wood can be scarce though...bring a good camp saw. Have fun!