I don't want to burst your bubble but I bought two of the stevens in .243. Both gave case head seperations. I won't have another ! One I bent around a tree in flustration and the other got traded to an obsecure gun shot 200 miles away. Yes, I sent them to the factory and they were repaired, returned and did the same think. (good service)
As to your handi rifle, I just bought one in 45-70 no problems, the guys on Greybeard say the .243 is the most troublesome of the lot. You don't need small base dies. Try polishing the chamber a little. But talk to the guys on the handi-forum at Greybeard outdoors.