Seems as if there are very few available shares currently.
Aside from having none available for the incoming suiting partner, apparently, there aren't any available for new investors or for existing investors who want to accumulate more.
This means that for there to be shares available, existing shareholders need to sell or shorts need to cover.

If existing shareholders sell, they will do so when they get their price. So they set an ASK price and once the BID price rises and reaches the ASK price, their shares are sold to the BIDDER and are owned by the BIDDER. This tends to increase share price.

If existing shorts have shares which need to be covered, if their contracted period has come and the short is required to "buy back" or "cover" their borrowed shares, then they will be forced to buy back at what ever the price is at the time. Since there aren't any available shares at current share price and only available at the ASK, shorts will need to cover at the ASK which will also tend to increase share price.

Could these next few days, with the initial days of the new president be the beginning of a long and sustained short squeeze, long enough to drive them out for good?

I feel we need to get this significantly higher, (like 10x higher) for over 2 straight months, held there by vast majority of staunch unflinching share holder base, restrained from selling into strength and the new 350 milllion shares to be "reserved" and unavailable for further trading 1 year after initial sale and only sold to parties willing to hold for 1 year (Partners).