Dialing in contour on the 1001RB-II (scooping out mids) coupled with the NEO 410 (already a bit mid-shy relative to other GK cabs) could be a bad combination, as others have pointed out. Maybe this is what you were hearing as "sterile", but it's hard to say.
Also, I assume you're using the 4-pole speakon cable, have the cabinet set to "biamp" mode, and have the bi-amp levels on the amp (woofer/tweeter knobs) adjusted appropriately. A common error is to select "bi-amp" on the cabinet but use a 2-pole speakon cable, or leave the tweeter dialed off. Either of those mistakes will defeat the HF horn entirely. Not saying you're doing this, just pointing out that it's happened before.
Blown speakers do happen and they can be fixed. But tone is subjective, and if you're unhappy, try something else.
In general, the NEO cabinets do pair well with the RB series amps; it's a matter of finding the one which meets your expectations. The NEO 410 is tuned lower than most other GK cabs, and as a result some find it "too boomy". Those people usually end up adoring the NEO 212 cabinet voicing instead, which has a "tighter" low-end and more mid presence. Most people find the NEO 115 to be tighter down low (more "hifi" and less "warmth") even than the NEO 212, but it will produce significantly less volume overall.
One other point: the 1001RB-II is a very powerful amp, and it delivers more power than its conservative rating suggests. That amp is well-known for blowing speakers, and can blow just about any of the NEO line cabinets if you aren't careful, with the possible exception of the NEO 412. So don't let the amp rating give you a false sense of security. We'll all give you the benefit of the doubt and assume that you weren't playing loud enough to do it, and you just hit an unlucky manufacturing defect.