When I got into the reloading business, the 22 Hornet was my first customer. I haven't noticed any real problems with. Probably the biggest factor was trying to put a crimp in while seating a bullet. If you do not have every thing adjusted correctly, you either do not get a crimp or you will crush the neck. I also would load the Hornet on a single stage press - that way if you feel any resistance while seating a bullet you can back off and straighten up the neck and give it another go. The single stage press gives lots of feel so you can back off when it does not feel right. I have successfully seated 100's if not thousands of flat bottom bullets, just make sure you give the case a good inside chamfer and go slowly when you seat the bullet (so you can stop if some thing does not feel right). Lately, (past five years) I have used an RCBS 222 Remington gold medal seating die, the one with a sliding chamber. I just start the case into the die until the sliding chamber starts to rise and drop in the bullet from the side and bingo in it goes real slick. I just needed to buy an extended reach shell holder for that die.
The older H&R Hornets were 1 - 12" twist, the newer ones are 1 - 9" twist. You need to use the tight patch and cleaning rod trick to find out which one you have. It will give an idea of what it will handle
BTW I had a SL 22 Hornet with 1 - 12" twist and it would not shoot the 36 grain Barnes worth a hoot. I think they were stabilized some what, they just threw patterns, not groups. I also have a Savage Model 40 with a 1-14" twist and it would not stabilize a 36 grain VG at all. Your twist rate will dictate how heavy (long) of bullets it will stabilize. Knowing Stimpy, he has an H&R and if it is a newer barrel it will stabilize or should stabilize 60+ bullets because of the 1-9" twist.
Good Luck and Good Shooting