Is it common to purchase a home with other debt?

Learn to control your spending and pay off debt.

If I create a debt fund that offers 9% interest on first lien notes with a 5-7 year payout, would that be attractive to high net worth investors?

A good DST would absorb the rest of your debt nicely.

I currently have no debt and make under $100k a year.

Can you do side hustles, cut down costs to get rid of these debts?

Interest rate determines the rate at which interest accumulates on each dollar of debt, and there's nothing magical about HELOC debt or amortized debt for that matter. 

Or do I just need to rent it out and accumulate more equity first?  

If I wait until accumulating enough cash in the account to buy another note, this will kill my yield.

I appreciate that, and you're right, any back-of-the-envelope calculation suggests that much of the wealth comes from the equity accumulation, even in the earlier stages of the amortization schedule.