I would like to replenish my cash I put in by doing a refinance cash-out and taking out some equity and using some of the cash-out proceeds for my next home purchase.However, I read somewhere that if I refinanced, I may have to wait 6-12 months from the initial date of the refinance as there may be a Owner Occupancy clause with the new lender.

What if someone decides to purchase a property in cash from the plan proceeds, but later decides to mortgage the property to gain additional funds to replenish the account for purchasing another investment property - keeping all loan proceeds and rental income within the 401(k) and making payments using only the funds within the plan. 

I do understand that I didn't account for vacancy/capex/maintenance/management, but as I was able to keep my initial capital so low, I set aside 10K in a reserves account that will replenish itself from rent payments.

I heard there's a 100k withdrawal allowance with no penalty and a 3 year grace period to replenish withdrawn funds.

Yes, you can delay payment but for a real financial plan I think you need to take that into account and if the renovation turns out to be more in the area of $30-40K, you will need to take a good chunk of your rent to replenish your HELOC.6.

Whenever you tap into the reserve you replenish it until it is back.

Ideally a 1m line of credit for acquisitions, funds secured by acquisition, with "battle plan" how at end of day once all reno is done and tenant placed they will roll property into it's own mortgage at 65-70% LTV, replenishing line of credit up to 1m again. 

We then refinance to replenish our HELOC. 

However you store the liquidity, bank, life insurance, investments etc. once you have the sufficient reserves you can take the Cap Ex, Maintenance, and Vacancy as Cashflow until you need to replenish the reserves.  

This gives you more time to find the right property -- as @Peter M. mentioned, buying investments that you can add value to and refinance out of, in order to replenish your LOC, will provide a powerful tool.