The refi is on a personal investment (real estate), not a business activity. That goes with the personal return. The loan to the S Corp is a personal loan "from shareholder." The S Corp does not pay the SBA directly, if it's not the S Corp as the borrower. If the S Corp pays the SBA, that's really a distribution to the shareholder. If there is a wrap around lending agreement, the S Corp pays the person, the person pays the SBA.

"Does it make sense to have the full amount of the loan issued to the individual?"

Here's what you stated: "the LLC, Scorp, and individual will all be on the loan and can be deposited into the entity of choice"

All on the loan is not the same as three separate loans. The LLC is moot, it's the person now. The S Corp is the only other entity, so if the individual is signing as President, that is person + Corp. If they are signing alone, they are the borrower and the debt is all theirs no matter what.

I read a lot of semantics here, but it's a shorter line between the points. It seems to be one person, multiple activities, not multiple start and end points.