I mount machinery to walls- similar situation. We drill the mounting holes, insert the anchors and then use Devcon Plastic Steel as a bedding compound to evenly distribute force. For something like a pullup bar, PL Premium or Premium Max also makes an excellent bedding compound and has the compressive strength, workability and ease of application you want.

The old fashioned solution is Rockite- it's used for bedding machine tools but it's not perfectly waterproof.