The three day period has been extended to seven business days a while ago. This means that you'd need to register in a place if you are staying there for seven business days or longer.

With your schedule, there is technically no need to register at all, provided you keep your ticket stubs as proof that you didn't stay anywhere for seven days or more.

The hotels would still register your even if you stay for just one night, but some don't even bother (I've seen that often in the provinces, not so much in the big cities).

There's no need to pay Gotorussia for this.