What are the options for mitigating problems with an asphalt garage floor
The DriCore subfloor panels are perfect for this.

Your main concern will be the tongue and groove panels separating, so if they are not firmly held on all 4 sides by the inner walls, install an outer frame of 1x4, or similar to make a tight box around the whole assembly. Obviously, leave the last side open until all the panels are in, then lock the last board in, or cut the last panels carefully so you can drop them in tight to the wall.
If you are worried about sinkage, pour sand over the floor and sweep it until the cracks stop taking sand, the leave a half inch of sand between the floor and the dricore.