Is there a way to do the initial block download over clearnet and then switch it back to private once finished?
Yes, you can do this. In fact, it’s the default behavior.
A fresh installation of StartOS and Bitcoin Core will download blocks from peers connected to over clearnet.
The setting you’re looking for to then disable clearnet is in Config → Advanced → Peers → Disable Clearnet.
I did an IBD, a few weeks ago, with clearnet disabled on a system using spinning rust(not recommended) and it only took 5 days to sync over TOR. Mileage may vary. I’m not sure how long it would have taken if I had not disabled clearnet on the initial install. But I suspect the bottle neck was the HDD, more-so than TOR.