I'm sorry to hear your BO is unsympathetic to your horses medical needs.
One thing I've done in the past is get a LARGE hay net that holds an entire bale. Put the whole bale of hay in the net, strings still attached, and hang it high and tight in her stall. Then, she has unlimited, mess free hay and no one but you is in charge of giving it to her.
As long as you're out 2-3 days a week, and your mare gets turnout, the bale should last.
Actually, apart from quality, hay isn't really an issue - I asked them to feed it to her ad lib as I always do at any barn, but for the first time in my equestrian life people actually take that seriously and I am yet to see an empty net.
I thought the problem was they refuse to feed her anything but oat hay?
You fill her net with a bale of hay you provide. Therefore, hay is no longer the barns responsibility. They can't say no to that.
I think that you could look at replacing the hay with either alfalfa pellets, timothy pellets, a mixed T/A pellet or alfalfa cubes, that will give her additional higher quality forage which she will likely eat before the oat hay. Also you could look at something like a safe starch forage (southern states makes a good one). This way your BO is happy because these are "bucket" items, not "hay" per se, but it really is hay in her belly.
I have a thing we call my horse's buffet for my ulcer horse...it's a feeder we made. We basically took 3 of the goat feeders with two sections and mounted them in a row on a 1x6 board. So you end up with a 3 foot long board with 6 little wells that each hold about 1.5 quarts of whatever. You put a screw eye on each side on the top edge and then mount it on the wall with double end snaps, either attached to screw eyes or baling twine loops.
You can fill each section with the different hay pellets, cubes, fat supplements, whatever...see what she likes and it lets her have that free choice in addition to whatever she's getting at feeding time. If you fill that thing up, you can easily fit 9 quarts of pellets in there...that's a LOT of forage by weight...almost 12 pounds of my alfalfa or hay pellets. IF you do that every night when you come out, she'll be getting a LOT of hay on top of the oat hay and she'll pick the pellets over the hay...
We are already giving her about 6kg of alfalfa cubes per day. I can't find any other "forage in a bag" apart from Alfa A, and between Alfa A and the cubes there isn't any different except for the price.
I'm in Portugal, so no brands you may know. I actually have been importing feed from England as there are zero low NSC formulas here... seriously, in an entire country, with tens of feed brands, and not one of them has something low starch.