That said, I'm not certain if the promise of better market rents (vs. what it's currently actually renting for) is good enough to influence the appraiser's valuation.

I give the best advice that I have at the time and if that is not good enough for  you, then I that is your issue.  

Personally, I'm looking for a good enough deal that will cover the cost of having the work contracted out.

So as long as your factoring that in your numbers, and have a good enough reserve for when that first cap-ex happens, there's no reason to be scared of an older property. 

I am personally of the mindset that anything can be "investable" with enough creativity and good enough terms.

We  are having trouble right now finding homes that we can get at a good enough price to cash flow in the current market.

You might struggle to get that second loan but you do, not for what you expected your preapproval is only good enough to buy an apartment in a good area that cash flows.

If you buy a good enough deal with built in equity, or put in a bunch of sweat equity the first year, you can refinance in to conventional and use an FHA 3.5% down loan on the next home... but Ramon is right in that you can only have one at a time.

If the HML guys (lenders btw, not loaners :P ) will not touch you due to lack of experience, one option would be to find a property juuuust good enough to get a standard Fannie loan, and let that be your first.

Oops, hit submit on accident....Anyway, if you get a good enough deal, the cash back from the refi can cover your purchase price in total.You'll have to put the cash upfront to close on the property, but generally seller - financing leads to lower closing costs than traditional financing.I just closed a seller - financed property 2 weeks ago and my closing costs were about $1100.Also, we check credit, but not income.