I only do the full court press occasionally.
That's not my objective. Given your original specs, in my opinion the BK2 is the best knife you can get for around $250. Of your original list, I think the ESEE 5 best meets your specified criteria but I like the BK2 better. The fact that BK2 costs less is a happy coincidence.
For those two knives, the steel and heat treat is about the same. In my opinion, ESEE's sheath is better but Becker's handle and grind are both better. ESEE's warranty is better on paper but in practice, they are about equivalent.
For your budget, you could easily get a number of great combinations of knives (BK9 and BK11 or BK14 or ESEE Izula - for instance) that *may* serve you better than a BK2 or ESEE 5 but that's not what you asked about. I'm trying to stick to your original criteria.
Others have mentioned custom as well I see - certainly worth looking at. You may as well get what you like now because, you'll end up getting it eventually.

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Beckerhead #42