We have offered to allow her to pay a reduced rent for the first few months as well but I am worried that may create some sort of limit on how much we can raise the rent on her in the future.

Offer aid and housing options if you're able -- don't try to profit. 

I'd like to use this to make an "all-cash" offer on a SFR, and then convert that to a conventional mortgage to pay off the HELOC.  

This allows you to access funds while keeping your existing mortgages intact.Second Mortgage: Explore lenders who offer second-position loans on investment properties, though rates will be higher.Cash-Out HELOC : While traditional banks often restrict HELOCs on non-owner-occupied properties, some portfolio or private lenders may offer HELOCs for investors.With $15-20K in liquid funds, look for deals where you can negotiate terms:Seller Financing: Negotiate lower down payments or interest-only periods.Subject-To Financing: Assume the seller’s existing mortgage while covering the down payment.Lease-to-Own: Lock in the purchase price while using rental income to build equity.

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I've only ever sent out an offer like that once, and that was to a preforeclosure lead that refused to discuss the property, instead telling me "that's not how real estate works, just make me an offer".  

I wish I had another work around for you, but I actually stopped using my business CC all together just to avoid the PITA "hacks" they offered as solutions. 

We offer a ton of different fix-and-flip programs including putting 10% down on the purchase price and funding 100% of the rehab.

It offers a lot more than just rent collection.

They tested the appliances thoroughly and offered a one-year guarantee.