I have a Finnor 9500 spinning reel and a Daiwa EXC6500T Exceler Spinning Reel. Both can hold around 500 to 600 yards of 100 pound braid. I have them on an 11 and 12 foot ugly stick surf rod. Around what size of sharks are the biggest I can probably handle with this setup?

Dont worrie what size can you get! Go fish,catch sharks. If something brakes you off upgrade your stuff. I catch 3 and 4 footers with 20 lb monno. I have been spooled too. I went up to 40lb monno. Worry more about getting your bait out using a yak or watercraft.
Best advice is use a long 5 or 6 ft leader. The 3 foot leaders are not long enough for bigger fish. They will turn and cut you fishing line.

Thanks. But I dont have a kayak and only go 2 weeks a year so it wouldnt be worth getting one.

How are you going to get your bait to the sharks?

Casting. I wont be able to get it past the "beakers". But people have caught large sharks casting where I fish at.