“you need to unroll it a tefach erev YT to avoid the issur of ohel/making a tent”
Actually, the thickness of the rolled up tarp is already more than a tefach wide; so you may not need to do any pre-unrolling if it rests on the inside of the sukkah.
Shloks are ok and manageable for small to medium size sukkas; otherwise I agree with golden mom and put the tarp/plastic cover on top of the table.
Also, I’ve seen entire sukkahs collapse due to the heavy rain water accumulation on parts of the shlok; not a pretty sight.
Best of course, if you can afford it, is the in-house sukkah with the roll away roof; but you’re pretty limited in sukkah size.