What method would you suggest is best for doing this short of paying cash or traditional financing...?  

They all prefer more traditional finishes.

In some cases, the demand is so high that the buyers would have to go through a lottery.

The only way to "get rich quick" is to win the lottery, lol.

That said, here are a few tips that may help with your decision.You can typically cash out your investments at any time, and lock in the current value, even in an existing plan.You could rollover the existing plan to either a plain old IRA (E*trade, a bank, etc) or a self directed IRA while you have access and consider your options with non-traditional assets in a self directed plan in the future.Within a self directed IRA, you have the ability to invest in traditional assets, so money does not need to remain idle.The type of self directed plan you would pursue is the big question.  

My dad recently retired, so he no longer has a traditional income, and though he has decent savings, his credit is spotty at best. 

ideally we would like one check as a traditional transaction, but the idea of 1500 month cash flow doesnt turn us off.  

Going the traditional route (i.e. not using creative financing) and assuming you have a W2 income that will fly with the underwriters at your typical bank, I can give you two options to start with.1) More Costly - Buy primary residence home with a 3.5-20% down loan, buy investment property with 20-25% down loan.2) Less Costly - Buy fixer upper property with 3.5% down FHA loan, 'house hack' by doing renovations while living in it for one year (to satisfy FHA loan terms).

And/or I guess I'm trying to figure out how do I analyze this differently if I were to pay cash for the property or if I do traditional financing with say 20% down, then bank loan.

These are usually targeted at bridging a short term gap that is not well served by traditional loan products.