do ask your take out lender though up front how they want to track the equity infusion .. 

Either way, it almost always requires an infusion of your own cash unless you're lucky enough to find a HML who will also finance your improvements.

California’s economy bounced back this summer thanks to an infusion of federal jobless benefits and business loans along with the reopening of some workplaces.

They don't need that kind of equity infusion, they wouldn't know what to do with the money, aren't great investors and is safer tied up in the appreciation of the MFR.   

Do I need to issue any "share exchange" or specific internal documentation to record this cash infusion in order to protect the legal separation of LLC vs me as an individual?

High crime and long term profitability are incompatible.All the four-plexes I have seen for sale required a significant upfront infusion of cash to correct long deferred maintenance.

However, the tax free cash infusion we got from the live in flip has allowed us to buy WAY more properties than we would have if we would have just continued to do live in multi house hacks. 

Homes of this vintage will have knob & tub wiring and a fuse box (typically screw-in fuses).If you find there's fuses, then that's what you will have. 

@Marc CelestinI learned the condo fee for Regency village is 310 per month and it infuses all utilities.

At a minimum your replacement cost would be around $3600 per unit.Obviously, this would be cost prohibitive for most investments and so generally you see budgets that show capital accounts with large infusions staged over extended times.