I haven't shot a Handi in .243 or any centerfire caliber larger than .223 Remington, but the comb of the stock may be what is whipping you. I had a T/C Hawken, still have it, and a Renegade in .45 cal. The .45 was absolutely brutal until I took a wood rasp and reshaped the comb to lower it a bit. After that, it was easy to shoot without pain. So, the Handi comb and your face may be at odds and that can be an unhappy situation. If you had a wood Monte Carlo comb instead of the plastic one, you could reshape it to fit you better and I'll bet that your painful experience will go away.
If it is hurting your shoulder instead, then you need a good recoil pad on it.
I have a Handi in .204 Ruger with the heavy barrel and the pallet wood stock set (with the Monte Carlo comb) and, of course, it has not been anything but a pleasure to shoot. But, in addition to the heavier wood stock, it has the 22" heavy barrel.
Post up a photo of it so we can see what your configuration looks like; maybe someone can give you some specific advise that will help.
One other thing I have noticed is that position and hold on the bench affects felt recoil significantly. If you are having to bend over to get down into position behind the rifle to shoot, this can make the felt recoil a lot more noticeable or uncomfortable. If this is the case try getting your rifle higher off the bench so you can assume a more natural position behind the rifle.
EJ