Re: How to know when the right time is?
Nicely done! IMO, when they start playing with no hissing, that is a fabulous, great sign. Myself, I think I'd continue the engage and play with them together, monitored for a bit longer before I let them stay mingled together all-the-time. I'd keep them seperated when I was away or sleeping. I think you could do the room swap, just be sure that both cats are comfortable being swapped into the different rooms.
Looks/sounds like you are very close to just letting them be together....good job.