> There's a difference in many US brokerages between having your stocks held in your name versus having them held in "street name" (i.e., in the brokerage's name).

This is irrelevant - a US brokerage cannot arbitrarily trade your shares, whether or not your shares are held in street name.

> GP could probably purchase the shares and be issued stock certificates that they could physically own, in which case there would be no chance of a brokerage being able to sell them.

This is equivalent to suggesting someone put their cash in a mattress rather than using a bank. The real solution is to find a better bank.