I have been thinking again

I have about 150 pieces of 357 Max brass that came out too short to use as 224GNR cases , so I said - self what are you going to do with these

and that started the search for a round bases on the 357 mag case .
Did a little looking and found the 22 Rem Jet and as H&R used to make a jet it should fit the bill just fine , I have an extra 20" 22 mag barrel that should work great for the donor , if S&W could get 2000fps from a 8 3/8" barrel I should be able to get around 2400fps from the 20" with 40 grain bullets .
I know that the jet was done in a .222 dia bullet but if i get a .224 expander ball all should be good , I can pick up a set of Hornady dies with form , sizer and seater for around $80 new or maybe a used set for about 1/2 that , I can kill 2 birds with 1 toss , get a new chamber and use my screw-ups at the same time . What do you all think of my idea ? Give me some input .
stimpy