Does the association just use assessments to combat the lack of reserves?
If this is your first place I would think hard about what this type of association management means to you. Often these assessments are thousands to tens of thousands of dollars and they have to be paid by you. They are recorded and assessed to the property if you don't pay, so even if you sell the property they get their money before you do. There is a reason FHA requires some sort of reserve requirement, IMO HOA's that have no reserves are not HOA's that I would want to be associated with.
To address your question, I do believe that you can acquire a "reserve study" by an independent third party that will "rate" the reserves of the HOA and the security of the HOA's liquidity. If the HOA that you want to purchase literally has 0 in reserves, this reserve study will not help you.
You can hit up family, friends, distant relatives, tap into any investment accounts you have, or pursue private money lenders to secure the extra 8% to come up with the 20% total. Given that your DTI is already relatively high, having to borrow additional money for your down payment, and then belonging to an HOA that has 0 in reserves the amount of risk you are assuming is substantially high.