This type of loan isn't looked favorably on by sellers. 

I’m sure the split won’t favor me, and that is okay.

This usually makes the marketability of the properties less attractive.It is generally not advised to try to assume a lease from a tenant especially if your state has favorable tenant laws. 

Chance favors the prepared, I guess?

This means after analyzing and initial due diligence, if your numbers worked even if you made an higher offer, make the high offer to fend off competition considering the terms and numbers are favorable.

To go a step further why not use the equity that you've already built up and divest from the property in favor of other, high growth investments?

I want to cash-out refinance and I want to lower my interest rate.I have no trouble getting loans on my investment properties, but those terms aren't as favorable obviously.

Furthermore, the tax treatment of passive income is different/favorable. 

Some quick thoughts I had while reading your post:HELOC your homes to cover the 20%Put your homes up as collateral (if you're confident you won't lose money, be careful)Open an account at your local small bank or credit union then they can offer you favorable termsYou can ask these lenders "what it would take" to lower the down payment. 

Does it have favorable commission splits?