My experience in seeing them, the bigger they are, the quicker they are removed! 

If you want to incentivise for a quicker deal, structure your offer so that the seller gets a better price or terms with a shorter acceptance time or closing period.

If you want it quicker (and usually of higher quality) you can often get it yourself (depending on the county) from their website.

OR buy in an area where the competition is smaller to enhance a quicker sale.

You could use the rental income to pay off one of them quicker - or re-finance.

The lot has the space, and I think the home would sell much quicker/higher with 3/2.

Or I could pour some capital into the property along with rent to bring the mortgage down quicker and refi later?

My thought is that once I can get one mortgage eliminated then the freed up cash flow will help to pay off the additional mortgage(s) much quicker eventually eliminating all debt, creating more cash flow. 

@Andrew Johnson   The current owner is managing the property on his own with VRBO.com.I am considering doing the same to keep the management fees and payoff the property quicker.

My dad is agreeing to a 1-2 year interest only loan on it, then when I refinance, we can then go seek out another property, rinse and repeat.Since I am in the starting stages still, his investment helps me get going quicker and allows him to have a consistent % income.He will be retiring soon and will be investing in buy & hold soon