If anything it makes you be more conservative since the deal really has to work and you can't tell yourself it's a good one because you're getting extra cash flow with no debt service.A true cash deal doesn't leave all the money in the deal, the additional cash flow will replenish the $5-6k/year you reference.

If you are planning on keeping the property long term, but need the cash now because you need to replenish your cash, use portfolio money (the stuff between hard money and banks). 

I wouldn't always advice taking it out of the security deposit as that can get messy later, but it is another option and you can request replenishment of security deposit (in most states I believe) after you have used it on a repair.

When you use that money, replenish the money. 

You could liquidate your stocks, buy it with cash, and then get a HELOC (or a cash-out refi) to replenish your stocks.

Ultimately, I want to purchase properties with value-add opportunities so I can refinance after fixing them up and "replenish" my HELOC which will allow me to repeat the process. 

We are using private money (business partners, family, friends and coworkers) plus our own cash to rehab a duplex and then will finance into a more traditional loan to repay the private money and replenish our stash.

What terms are you offering for security deposit replenishment?

Then, I refi said properties and replenish the funds.

Also consider a cash out refi payback plan to replenish all of their money within xx months.