Apply for non-entry grade to a different private, probably won't find out if there is spot until late January or even Feb. Is it possible to hold off sending current school records until we are certain that there is a spot? Trying to minimize the impact on the relationship with the current school. Thanks!

Can you ask the target school?
As a parent, you should be able to obtain the records. Why don’t you send them to the school you are applying to as part of the parent statement and at the same time ask if the official report from the school can be delayed? That said, it’s highly unlikely they will waive the teacher recommendations unless this is for a very early grade
Families switch private schools often enough that the schools see it regularly. I don't think a school would be too concerned about it. DC switched privates during an entry year and everyone was supportive with recommendation letters. We asked the registrar to send the transcript and didn't have to ask the teachers or deans for the transcript.