A couple of thoughts:

1) Regarding your statement on x/c hands I would consider you examine your strategy. If your x/c range is all Kx and middle pairs you will be severely capped on a lot of turn cards (diamond, Ace, etc.) and have a tough time against competent opponents. If this strategy has proven successful at the current stakes, it will prove to be a very exploitable leak if/when you move up stakes.

2) If you are using this sizing on this board texture against calling range of CO player, I prefer x/r this hand. We block A high flush draw hands and our hand needs less protection than AK no diamond, I could even be convinced that we could x/c this hand having the A of diamonds. Other x/r hands include KK with no FD. To protect x/c range throw in KK with the K of diamonds. Don't worry about overplaying the hand - focus more on playing your range and what lines you take with certain parts of your range.

3) Regarding the above point I believe (though I may be wrong and if so would appreciate input) we should have a range advantage on this board and can employ a high frequency c-bet strategy for a small sizing (~1/4 - 1/3 pot). Villain likely has suited and (some off suit) broadways, pocket pairs, and middling SCs a good portion of the time and very infrequently will have top pair here (yes KQ and maybe some other suited K broadway hands that didnt elect to 3-bet but we block K x hands here).

Hope this was helpful.