In my .577 rifle I tried 4350 and it was a miserable failure, with misfires, bloopers, and lots of unburned powder left behind on the loads that did go off. In all fairness I may not have reached a good enough load density with it, but it was causing so much trouble that I gave up on it.
If you want to try a Reloader powder, I would suggest Reloader 17, I think the 22 is too slow for good clean burns. I wound up using H4198 but I'm not going to tell you how much, you need to start low at around 60 to 65 grains and work slowly upwards from there.
I know 5744 will work but I have no experience with it in the .577's. Benchmark was also a recommended powder but I never got around to trying it yet either. 4895 or 4831 would be my next choice of powders to try, if I were still not satisfied. Good luck with finding that special load that your gun likes. Bob