Unfortunately they will keep trying to nest. Usually removing their nests does not deter them. Even if they do give up by that time your bluebirds will move on to another box somewhere. And yes, he’ll move on to the next box you have. They are also known to retaliate when their nests are removed or unsuccessful…or so it seeems.
I understand your sentiments on not killing them. When I first started this bluebird hobby I couldn’t kill them so I would take them far away and release them but then became aware that was frowned upon because I was just causing some other bluebird host issues. I finally decided I had to dispose of them. It is hard even now but necessary.
In my opinion the only way to get rid of this current problem is tontrap that HOSP pair with a Van Ert trap and then eliminate those HOSP.
Tammy