That reduces your tenant pool a lot and can make hard to find good tenants. 

Lender regulations certainly come into play, but even for non-levered syndicates it is desirable to have a max in your mini-max to reduce concentration risk. 

I have not accepted cash for more than a decade, reduces the chance of being a victim of armed robbery or counterfeit bills.

One thing I have not really seen touched on is how to best handle BRRRR when there is any significant amount of time left on a tenant lease.Any experience or insight on how to best purchase or manage deals with pre-existing leases in place to reduce time it takes to get to re-fi?

(My initial thought is take the reduced risk and go cheaper on our first one knowing we can always buy more expensive next time, but I also don't want to pass up “great” deals if they exist.

Then, when you file your taxes you can include depreciation on the property as an expense to further reduce any taxable income you might have. 

When I went out to inspect, found he didn't have the energy to shave and get a hair cut either.

@Cody Mau House Hacking in the LA area can work to reduce your living expenses while building up your wealth.

@Trey JonesThere are a handful of grants and options that can reduce downpayments below 3.5% (some combination of grants or forgivable 2nds) but (and don't quote me on this because I'm not a lender) I think they are all limited to single family residences. 

Use the cash from your non-1031 sales to reduce debt on the replacement side.