Different lenders/banks have different seasoning periods--i.e. the amount of time you must wait from the original purchase in order to refi--but it more than likely will not have to be 2-3 years if you have the equity available sooner. 

You are not allowed to rent my property to other people, period.

We also purchase with no inspection or contingency periods; which also makes our offer stand out better.

For example, if I buy a property from a wholesaler at a discounted amount, say 100k and the property needs 20k in repairs, and the property should be worth 150k when finished, if I buy it for 100k and only put 20k into the repairs in a short period of time, we have seen appraisers appraise the property lower than it should be appraised for simply because we bought it at a good deal.  

Any help you can provide me with during this period would be welcomed!

Occupy the home for a period of time and then convert to a rental if you decide to live elsewhere.  

They have been wonderful tenants...period.

In my 30 years, I have seen where franchisor’s have deals where you may have reduced or no royalties for a period of time or until a certain weekly sales average are met - but not often.  

Some investors I work with only use the hard money for the acquisition to avoid the fees and inspection delays during the construction period, when the lenders provide construction draws.

Maybe try it with only one of your rentals for a short period of time and see how it goes?