S-Corp Contractor builds his own home

"since he will put his name on the title?"

"At some point his new home could be an asset of the S-Corp."

Well, which is it? Holding real estate in an S Corp is the worst way to own a property. If it is his own residence, why are you/he bringing the S Corp into the loop for ownership?

"Credit his home on the P&L or Balance sheet and debit Distributions?"

Nothing hits the P&L.

"As he accumulates expenses to the building, these costs would increase his asset "Personal Home"."

It's not his asset if you are entering this in the S Corp and he isn't paying for it personally. An S Corp doesn't have a Personal Residence. You seem to be trying to commingle everything in error. Either it is a business project, or it's personal and should not run through the S Corp at all. In which case, worker comp would like to have a meeting.

The costs accumulate in Construction in Progress, an asset. Or, everything spent is a loan to him, that is an asset as Loan to Shareholder. That will include land, labor, materials, subs, architect, engineering, permits, insurance, anything related to the project. If he is working under a construction loan, the interest that also is not expense.

Credit bank or credit card or AP, Debit instead of Expense is now Debit to this accumulator account.

If anyone is taking out a mortgage, who will that be?

"so he doesn't have a tax liability"

It's a pass through entity. You can't expect this project to throw them into loss. And you don't know this until the project is complete, the accounts are settled, you compare to his basis in the entity, if there are still any debts on the books for the project, what is in retained earnings, are you treating it as loan or as distribution, etc. Tax liability is the final result, not the upfront concern.