Why? 45 fpe is not an obvious energy for 25 caliber. You'd have to push a 25.4 up around 950 fps to get there and accuracy would almost certainly suffer. But it's only about 775 fps on a 33.95. If you want to shoot heavier pellets you would want more like 50-55 fpe to get the up over 800 fps for a flatter trajectory. If you want to shoot the lighter ones upper 30s to low 40s would keep them in the recommended upper 800s.
Anyway, to get that many shots at even low 40s means you want a bottle gun. Not a lot of them in the price range you specify. I don't think the Blitz is regulated so while it may give you that many shots what will the velocity variation be? Do you care? If you want a lot of shots at low velocity spread you want a regulated gun and one with a regulator and a bottle may push you above your price target.
If you could live with more like 40-50 shots, I think a P35 in 25 would do it and it is easily in your price range at under $500. There is also now a Stoeger Bullshark which seems to be the same gun in a different stock. I have mine tuned to shoot FTTs (20 grain) at 875 so low 30 fpe and I get 60-70 shots with an ES around 15 fps. I detuned it to this level. I did not want the FTTs up over 900 fps. I'm sure you could get 25.4s over 800 fps and you might get 33.95s to 800 but shot count would suffer. The barrel length is only 450mm, about 18 inches. Gun length is under 29 inches. Weight is only 5.2 lbs.
I think in terms of getting pellets in the selected caliber up to 800-900 fps. Whatever energy that is, it is.