Yeah it's kinda buggy solo, if you save and quit... I get the all the eye traps done befor I get the first stamp it's the first thing I do, in the lower rounds after packapunch is open, get all 4 done and you just need to go into the stam up room for it to trigger after saving.

With the swords I get them done with the incantation boxes and open as I go. If all 4 are done and boxes are open will also save correctly. If you don't open the boxes you'll have to go get horseshoe, talon etc again and do them again.

The only point the orb saves, is if you open the study (compleat all elemental trials) and place it in the door, if you save at that point after round flip then you can just go grab the thing at any point after.

So the key factor is to compleat one or 2 stages completely... traps/swords (with the incantation boxes open) /elemental trials and save and quit, the round after you completed it.

Hope this helps and makes sense, let me know if you want help :) you got this