Most sellers will accept an offer contingent on the successful closing, especially, if you are beyond the inspection period. You will need to provide documentation verifying the contract and buyer approval on your current residence. Right now, inventory is very low in the Columbus market. If the seller receives a strong cash offer, that would be accepted first. In the areas you are looking in, we are having bidding wars. Once you find the home you like, I'd advise you to make a full price offer so it gets accepted right away.
Where are you moving from?