It is still early days at one month. Personally I would just assume that the horse has a significant soft tissue injury in its foot or pastern and give it a longer period of rest and rehab accordingly. More like 2-3 months of rest, at least, and possibly up to 6 or more depending on its progress. I would definitely do a full set of foot x-rays before-hand, if that hasn't been done already. Unless you are insured or have pretty deep pockets and would be willing to undertake expensive specialized procedures, that is probably where you will end up after MRI anyway.
I usually give my vet one try before taking him to a specialist. I've found way too often that it would have been cheaper in the long run than go around in circles with my vet. And he's a great vet. I don't know where you are but there are a ton of great places in Va and that area.
This may sound too simple.I had a horse years ago that turned up lame for no known reason.We would. bring him out every day or two and check for improvement and there was none.Before going through all the vet X-rays,ultrasounds and blocking we decided to leave him on stall. Rest for 7 days.Brought him out after 7 days and he was sound.Recently had one turn up lame at a show for no reason.He was on stall rest for the rest of the show 4or 5 days.This horse was sound when he got home.Some time all it takes is time.I've seen horses that need much more than stall rest,but I always try that first.I have been lucky to have horse that are happy to sit in a stall as long as they get plenty of hay.