Looks pretty basic. I haven't done a brake job on a 1710 but this is from CNH parts online and it looks very similar to other compact tractors I've seen. Pull the cover off and the brake shoes are right there, very similar to a basic setup on an auto or motorcycle....the shoes are easily removed. I have had similar experiences to what you described ( brakes no longer function w/adjustment) and so far w/o exception, when I open them up I have found that there has been plenty of pad left but the shoes and hub are glazed. I have has great luck with sand paper and a wire wheel on a drill or angle grinder removing the glaze ( wear a mask) and a good shot of brake cleaner on everything. Not saying this is your problem but from my experience I would say you have a chance that may be all it is.
If not, it looks like the shoes are still available from any Ford/New Holland dealer ( Messicks has them for $135) or you can get the shoe bands relined w/ material at local clutch/brake shop.
BTW: CNH parts online ( kind of hard to navigate at first) or Messicks is a great way to look up diagrams like I posted...type in your tractor model number and look at very detailed diagrams of whatever you need.
