of the night, not remember the step is there, and trip over it.

Her mattress is very high, actually I think its a double mattress. She has a little plastic stool that she also uses.

Dunno why, it worked for me, didn't forget, fortunately. Maybe the answer is Don't Worry??? Have a night light nearby?

I put an old step exerciser at the foot of the bed and he uses it to jump up on the bed. It doesn't bother me because I get in and out of bed on the side.

Could you put the stool at the foot of the bed? This way you would not mistakenly trip over it when getting up in the morning.

don't require a box spring any more. Are you still using the box spring? Try to find out if you don't need it any more and discard it. That would solve the problem.

Another solution could be a new bed frame which is enough lower you no longer need the stool, but that's a much pricier solution.

is that it's easier to stand up from a higher seat...

On entering a room I do a quick scan for the highest seat before choosing where I'll be.
There's nothing worse than a sunken sofa or chair, where the derriere is lower than the knees.

Old beds used springs under mattresses which were thinner than our box springs. Also, the mattresses were about half as thick as modern mattresses. My antique bed with it's modern mattress set also doesn't look right as it is not in proportion with the head and foot height. Then of course, there is the stool problem. I do have a good antique foot stool which is upholstered on the top, and is larger around than the usual step stool. You can find those pretty easily in antique shops.

Has anyone explored the possibility of finding a thin box spring? Or a thin mattress? I could replace either or both.

to get the blood back into upright mode.
that should give you enough time to figure out that the stool is there.
While sitting, move your legs or feet around a little to feel what's underneath.
I think you'll be able to handle it just fine.