Benchmade Small Summit is another handsome deep carry lockback knife that is just a bit over budget, 3.65" closed, and 3.04 oz.... Very close to hitting every spec. But, nail nick for two handed opening, however you can add a $5 Kwik stud, (silver or brass), place the studbwhere you want it to best suit your grip and thumb placement, and presto, you have yourself a great looking diamondwood, one handed opening, deep carry clip, lockback knife in s30v Steel, that is only 0.05" over length, and 0.04 oz. over weight!
Should run ya about $125 in all.
That's a great option I think to really nail everything you want, except the handle, but the wood looks way better then any G10 or FRN handle IMO...