Then, set up an annoying alarm that starts beeping after it's been open more than 10 minutes. 

We have a decent amount of savings, at least enough for a down payment and closing costs on our next home, but the buying power just seems so limited in our area. 

Kind of limited in my avenues haha

I use the Zelle app to collect upfront money from tenants and it is instantaneous with no take backs but it is not automatic so I doubt you could set it and forget it.

If you are solely searching MLS and not looking off-market, you are limiting yourself.

If the duplex is listed at $515k, you could probably qualify and use your VA loan for the unit you are living in, and they will be able to use the projected rental income of the second unit to cover that difference. keep in mid that loan limits vary by County. 

Whether you pay off the properties or keep them, don't forget that you can do a cost segregation study and use bonus deprecation to off set taxes.

Rather set $300k on fire than pour it into a condotel,  the condotel will cost you more to get out of.  

I do know of 0% down programs but only limited to 1-4 units.

Side notes here to keep in mind, the market is crazy right now and lenders are prioritizing home purchases vs. refinancing due to limited labor availability.