I think you have a common problem. My boarding contract also says they'll hold the horse for the farrier (and doesn't specify it's only for the barn farrier). The barn farrier generally doesn't have anyone hold the horses for him- there's a whiteboard with a list of horses to be done, he gets the horses himself (they're stalled, so it's not like he has to catch them from a field... if they're in turn out I assume he would ask someone to bring them in or just skip the horse and try again later), ties them, does his work, then puts them back.
I also don't use the barn farrier. I try very hard to be there every time my farrier is because I want to know if anything looks off even if my farrier wouldn't think it's a big enough deal to call me about (for example, I like to know if there's bruising on the sole) The last time I wasn't able to meet my farrier, so I asked if someone could hold my horse for him. I couldn't get a confirmation so I let my farrier know what stall he was in and said if he felt OK getting him out himself to go ahead and do so and I'd leave a check for him; if not we could reschedule. The morning of the appointment I got a call that someone would in fact be able to hold my horse and texted the info to my farrier, but he didn't even bother- he just got the horse himself like the barn farrier does.
Would I have been upset if I had to delay my farrier appointment because no one could hold my horse? Yeah, but it wouldn't have been a big deal. Lots of little things like this can certainly add up to a reason to move, though.
If you do have to hold 2 horses again, it seems like it would be a good idea to just assume the barn staff won't bring them up to the smaller paddock for you. Just get there early, and if you can put a 3rd horse in with them so they won't get so upset when one is taken away for shoeing.
I look at this way, and its probably not what you want to hear. Its your horse, your promise to your friend, its your responsiblity.
If you have to pay for full care board, someone else Does everything to care for your horse, then you dont have enough time to own a horse.
That's really not fair. There are lots of people (myself included) who wouldn't have the time (or land) to own a horse if it weren't for full care board. Just because you're paying someone else to feed your horse twice a day, turn them out and bring them in, doesn't mean the horse's care is suffering, and it doesn't mean you're not an involved as someone who cares for their horses themselves.