Should I add sand or more limestone crush to raise a patio with no gravel bedding?
I wouldn't call that a typical base, but if it was properly compacted, it should work. The typical base is pretty much what you described:


topsoil dug down to undisturbed soil and/or topsoil dug out then soil machine compacted
2" layer of crushed rock, machine compacted
2" another layer of crushed rock, machine compacted
repeat until you get to 4" or the desired height (if above 4")
1" sand, leveled
pavers


Note that in this system, you're not designing for permeability or drainage at all. If you are using pavers, this is hardscaping, and is meant to shed water, not absorb it. To properly shed, it needs to be properly sloped. This is true for the base layer as well. 

The purpose of the base layer is to create a solid, stable surface. Ability to drain is desirable (to avoid frost heave) but that's secondary to providing a proper surface to shed water. 

In your case, it sounds like you already have 4" of compatible material. I'd do the following:


remove pavers
rent a compactor and compact existing base
add additional base material and compact to get the slope you want
add sand
put pavers back
add locking sand to joints


the big catch here is that this will ultimately raise your patio next to your house several inches. If that's tolerable, you're good to go. If not, then you have to do the reverse...instead of adding material closer to the house, you need to take material and remove it further away from the house. This will reduce your total base at the outside edges, though. That may be acceptable in your case.