Make sure software monitoring is turned off. Reaper should compensate for playback latency automatically.
I've never been able to calculate it accurately on a consistent basis. Its faster just to slide the clip into place.
Are you using the Axe as your soundcard?
When I reamp using my RME Multiface there's no latency.
I did a test on my PC with Reaper. Reamped a test track through the Axe via USB. Picked I high CPU preset (89%) and bypassed all the blocks so the resulting reamp would be as close to the original as possible. I then zoomed in and measured the time difference between two identical peaks in the tracks and I got 12ms on my system. I did it again with a preset with all shunts and got basically the same. Not sure how this would compare on other systems, but the latency is there although very small. It should be simple enough to just include a loud string pop at the start of your track and then zoom in and use that peak to align the reamp to the original. Sort of like using a clapper board to align audio and video tracks.