Many times with the senior horses, it isn't fat calories they are missing but protein.
If she isn't allergic to soy, buy some soybean meal and add it to what you feed her in the morning.
Soybean meal has the highest amount of protein and amino acids of anything.
I feed my 25-1/2 yr old Arab 1/8th cup during the warm months and double that during the cold months.
I also give him 1-1/2 lbs of well-soaked timothy/alfalfa cubes twice daily, but that is a lot of extra feed to shove down her when you can only be there once a day to hand feed her. So I would try the soybean meal and see if it helps.
I could easily see her getting trapped in a chute - either because someone is pushing her forward from behind and she can't go anywhere except over the top (and get hung up) or thru it (and get hung up) or kicked to death since it's obvious she is weakening and losing her alpha-dominant role. Also, if she has arthritis it's too difficult for her to back up.
I really understand your current dilemma but, I am sorry, I just really think an un-attended feeding chute is a bad bad idea for a horse. We only used chutes when we were loading cattle.