You can raise cash via debt or equity and via institutional or private means.

Could private lenders be the solution?

As long as you give the proper notice to the tenants, you should be fine. 

Investment Info:Large multi-family (5+ units) private money loan investment.

I also notice a lot of people from Chicago moving into the area (myself included) due to the movement towards remote work, although this is anecdotal evidence.

A pretty common way is to go through a private lender.

How flexible is your lender when it comes to LTV, and have you ever considered how private money lenders can offer more competitive terms?

The goal is immediate cashflow that will quickly increase as we fix-up and/or lease up the properties, which ultimately will lead to a higher property value and a cash-out refi within the 5-year term.Do you happen to know of any good portfolio, bridge, and/or DSCR lenders, private or otherwise, that may be willing to work with such a scenario?

Give them notice of rent increase.

Besides traditional banks to access the equity via HELOC or refinance, what other programs are there via private lenders that will allow me to access that equity?