How to anchor through .5 inch drywall/.75 inch wood/concrete block

I would drill a slightly oversized hole through the drywall and wood, then drill full depth in the concrete for the sleeve anchors. Set the anchors flush with the surface of the concrete.

I would then use over-length bolts into the anchors, at least 3". For extra stability, I might put a metal spacer in the oversized hole in the wood and drywall, and have the bolt pass through it.

This sounds like a perfect use of Tapcon anchors. They are hardened steel screws that actually thread into concrete once an appropriate pilot hole is drilled:

I'm not sure if such a specific product recommendation is bad form on this site, but I'm not sure of a more "generic" approach.

Since these are threaded, they will use the 1x2s and the concrete block for strength. Going through the drywall, then an air gap, then the block might be a bad idea unless most of the other screws are going through the 1x2s. If you can't screw the mount to the 1x2s because of their location and/or spacing, the canonical solution is to screw a between the 1x2s then screw the mount to the boards.

Use a "wedge type" expansion anchor, you can buy them in lengths that will work fine for your application, assuming the block is filled, not hollow. Try a builder's supply store instead of a "big box" store. Hollow block would require a different type of anchor like the second picture.

Per the manufacturer of one type: "Versatile fully threaded design is standard on sizes up to 3/4" diameter and 10" length."

I use E-Z Ancor Twist-N-Lock Drywall anchors to mount pretty much anything to drywall. The hard part is when you are dealing with drywall over concrete block. The concrete block will always prevent the anchor from going in all the way. So you have two choices pre drill the hole with a Masonry drill bit that will allow the anchor to fully seat into the drywall. Or you can use one self drilling anchor to start the hole until you just get to the concrete block then back the anchor out use side cutters to trim the anchor to remove the self drilling part then seat the cut anchor and install a shorter screw. I have done this method to mount a 65 inch Samsung and a floating shelf system that holds all my Audio Video equipment including two AV receivers a cable box and center speaker just my Yamaha Receiver alone weighs 70 pounds all of my equipment weighs a lot when combined but the weight spilt through many anchors even modified anchors holds this equipment and probably much much more with no problem. If you get lucky and hit a wood strip just predrill with a tiny drill bit measure how long of a screw you need and just use a deck screw not a weak drywall screw.