Mid time engine searches can be discouraging because the prices are governed by the certificated engine market. If you need a replacement engine for your Cessna and you look at $35,000+ for new, you might think $15,000 for a mid time used isn't a bad deal. But for an experimental, when you can get a new engine from Aerosport & others for a little over $20K, that used engine doesn't look so good.
If you shop a lot, you may eventually find one at a price you feel is acceptable. There is an O-360 on Barnstormers right now 0-SMOH, overhauled by Barrett for $16.5K. Probably has been overhauled at least once before for that price. I found a 250 TTSN O-320 for $13.5K.
You could nose around at hangars, asking if anyone knows about any available engines. Networking like this could be pretty productive & you get to meet a lot of other pilots. And there is a salvage operation at Deer Park, outside Spokane that might have or get what you need. He had an O-320 a few weeks ago for $11.5K; I didn't ask about an O-360.
Consider carefully how you will work the transaction for a used engine from a private party. You could send a check and trust the seller to ship it, but what if he just takes your money? What if he does ship it, but it isn't as described? Or will it really be crated adequately?
For mine, I drove to from Oregon to Colorado to pick it up, and that is about the max distance I would consider.
How are you going to pay for it? I arranged with my bank for a debit card advance (some banks charge hefty fees for a large debit card advance--mine doesn't charge anything), we went to the seller's bank for the advance & it didn't go thru. Probably bad timing on between computers at the two banks. And the policy of the seller's bank was to try only once as a fraud prevention measure. He looked at me and decided I was trustworthy & volunteered he would accept a personal check. The remaining alternative was a wire transfer, which costs $20 and takes a few hours, it was 2:30 in the afternoon & I would have had to spend the night there & finish the transaction the next morning after the bank opened. You could bring a cashier's check, but if the seller is wise he won't accept it because they are being counterfeited left & right these days.