My experience in real estate has been limited the purchasing of my own house. 

However, the rule does not require implementation of the AML Program rules for non-profit organizations that: (1) limit their activities to assisting with the preparation of loan applications or referral of prospective borrowers to qualified lenders, for free or for a fee, (2) provide short-term, non-mortgage loans to qualified borrowers or homeowners, or otherwise “facilitate” the extension of a residential mortgage loan (but do not make the loan or offer or negotiate the terms of the loan).

If all of your cards are with just one or two banks, your financial risk increases because you cannot transfer balances within the same financial institution...in other words limited bail out strategy. 

If you have equity built up as @Shawn M. has stated you can refinance in to a conventional mortgage. (75% LTV for a conventional rate and term) and then use your FHA mortgage again, and repeat doing this up to 4 mortgaged properties total as this is the limit for FHA.

But I am wondering if I am limiting my potential tenant pool?

Thanks @Justin R. and @Steve VaughanI know this was limited info, but since it's not a real deal right now, I was hesitant to say too much.

A lot of what you're seeing has to do with market dynamics: increased competition, limited supply and REO trading direct to hedge funds/PE through private deals (vs auction or MLS).   

My question is, would it be better to try and pay off each bill slowly, paying what I can on each every month, or getting a new credit card with a higher Credit limit and condensing all of those bills onto one if I'm able to do so?

Dont allow people tell you skie is the limit.

There are so many out there that its hard to say with the limited information given here, what the best way to structure the deal would be.Another thing to consider is what are your goals in real estate.