I think that the "seasoning" period you are referring to, is related to situations where an investor puchases a property, rehabs the property to add value, and THEN refinances at a new, higher valuation.
For example, if you were to purchase a property for $300K, put in $50K to rehab the property, and then claim that it is worth $400K, the lender might not be willing to let you refinance at the $400K valuation until a seasoning period has passed.
Lenders often require a seasoning period for refinances at new, higher valuations, after purchase.
But, if you purchase a property for, say $300K in cash, and the appraisal supports that valuation, there's no reason I can see that a lender won't lend against a $300K valuation today.
I'd call a couple of lenders, and I'd expect that you are able to get a cash out refi without too much trouble.