Leveling a Subfloor

I’m converting half of my two-car garage into a playroom for the family. The garage is built on a sloppy slab that sags several inches through the middle where water is known to collect. I’m having a trench drain cut into the garage’s opening to prevent this inevitable mishap from occurring under the new room, but I’m left with a leveling problem that I need some tips and tricks for.

So far, I’m having pretty good luck with my current plans, it’s just tedious. I am raising the level of the subfloor to match the house – I’ve measured down from the finished ceiling to find a point roughly 8’ down including the eventual subfloor panels. Below this point, I’ve added 2×4 PT boards on-edge on top of sleepers which I’ve secured to the concrete. The 2×4 baseboards had to be tapered in order fit a level line under my 8’ (8’ 3/4”) mark. In adding the joists between these boards, I’m leveling and shimming each one over two sleepers (roughly 41” apart) and the joist caps. This is the tedious part. I seek level from the previous joist, and along the length of the current joist. The first few had to be tapered to fit, though as I get closer to the center of the concrete, I have an additional 2×4 attached to the sleeper. It’s not impossible, but I grow concerned as I move across the floor to the other side of the wall; further away from one reference edge to somehow land on the far sided one. Is there some sort of trick I can use to get all of this leveled up accurately and my joists shimmed quickly?

-- It takes a viking to raze a village.