I second the Rock Chucker suggestion!
I have a Rock Chucker that was already pretty old when I bought it used 30+ yrs. ago, and it's still working as good as new. I also have an RCBS RS2, which is an "O" frame press, but it's cast aluminum, and that press has been worked hard for a good 27 years or so. Both presses have seen a lot of bottle neck loading. I have no doubt either of those presses will out live me.
Actually, the Rock Chucker has a chunk of threaded steel missing in the same spot as on your Lee press. It was broken off when I bought it from the previous owner. From what I can tell, the previous owner must have stuck a case, and then tried to remove it by either hammering on the handle, or just brute force. I suppose I should have RCBS send out the new piece one of these days. But even now, and all these years later, it still works fine, despite the weak spot where the handle threads in.
GS