I've been going to beavers bend all my life. We've camped there every Thanksgiving for the past 22 years and camped there random weekends before that.
Not sure about stripper but I've caught LMB and I believe there are smallmouth. The river in the park will be crowded with canoes, kayaks and tubers so I would suggest fishing either outside the park on the river or fish the lake.
If you're taking your kayak then definitely hit the lake. There are a lot of good lmb in there. Throw some big chartreuse rattle traps. If you're looking for smallmouths then hit the nearby Glover river and throw crawfish cranks. The state park will be full of tubers and people chasing trout. My buddy has pulled some nice trout out of there but the bigger ones usually feed at night.
Lower Mountain Fork - Spinning set-up with rooster tails, you'll catch all kinds of fish. I wouldn't go any further than the Rock Garden or put it under the bridge where you'd normally take out and go up stream where the last set of Rapids comes down and fish around in that current.
There are smallmouth in the river and in the lake. I went last year and had a blast on the river fishing for smallies. If you are going to fish the river you need to get started before the shuttles start running the turons to the launch point. I believe they start around 9 to 10ish. You Cuda should work fine on the river. I took my coosa and it worked great. The rapids are not anything to worry about if they are not releasing water.
Yes you can, I'd put in below the Re-regulation dam and just fish within a half mile or so of that stretch, that away you can paddle back up to your truck. (There might be a few little spots you have to get out to get back up) but they're not too difficult. I'd put in as early as I could, like at sunrise and once it starts getting crowded on the river maybe head over to the lake if you're still wanting to fish. There's a little boat "ramp" you can unload at and then just park off to the side out of the way. Last time we were up there we did the river twice from there to the bridge at hwy 70 and that little stretch was were the major majority of fish and quality fish were caught. Don't bring any beer in your kayak either, if they catch you, you'll get a ticket. We wore'em out with little rooster tails, orange with gold blades, weightless senkos would probably work good too. Keep everything tied down when you're not using it and don't get in a rush going through the big rocks and you should have a good time. Here's what it looked like last fall, might be alittle different with the rain and what all they've gotten.
/\ /\ What NoconaBrian said for the lures. Add to the list small Pop-R's and small topwater frogs.
When I went I unloaded at the Re-regulation dam and had my fishing partner wait there with the kayaks while I drove to Ambush adventure and had the owner ride back with me to take my truck to the take out point at the hwy. I think I paid him $10 for the help. He left the keys locked in my truck while I had the extra set. I had set the arrangement up with him before the trip. I am sure you could also pick him up before unloading the kayak.