This was my experience with Lewis:
When we got Lewis his nails were way too long and he would often scratch me and leave long red marks down my arms. He wasn't a confident dog and I didn't dare try to trim his nails straight away. I think he really didn't trust us and didn't understand why he couldn't go back to his old owners.
Lewis needed a lot of grooming but he was very nervous about being brushed (which I understand because it probably did hurt a bit dispite all efforts to be gentle). I had to do two or three 5 minute grooming sessions a day and it took a couple of days to get one leg half done then I'd give him a day off then start on the next leg then return to the first leg etc. It took a couple of weeks to get him good and now I can get him completely brushed in about 10 minutes (I brush him (and Holly) 2-3 times a week so he never has knots to work on).
At the start he never actually snapped at me but he did the quick head movement towards my brush hand that could have easily been a snap and I had a leash on him that I tied to a chair so he couldn't reach me (although the leash was a bit slack so he didn't feel trapped) and I constantly watched his face to see if he was getting too stressed. He is a bit of a snappy dog at times so I really didn't trust him.
In that state I decided I didn't want to risk doing his nails incase it
did make him snap. Dogs seem to often object more to getting their nails done then being gently groomed. I think if I had gone straight to the nails it could have damaged the trust I was building with him and made it hard to not only cut his nails but also groom him.
But by the time I had his coat in order he trusted me a lot more and I trusted him more (I had stopped leashing him for grooming by then) so I decided to have a go at cutting his nails.
The first time I tried it I had him leashed with someone else feeding him really yummy treats. Then I clipped one nail (I think it was a back one) and watched carefully for his reaction. He was fine and I was able to cut all his nails in one go (I didn't cut them short, just to about half way to where they should be). Then a week later I did it again (on my own) and he was fine.
I don't know if Lewis would have been fine with his nails being done all along or if the time spent grooming him and gaining his trust was essential (I suspect the latter).
So I would suggest that you could first start with grooming (if you don't groom Brody already). I find grooming is a good way to calmly bond with Holly and Lewis and to let them really trust me manipulating their body and touching them everywhere. I groom them on my own in the kitchen away from everyone else. Although they clearly look forward to being groomed and do get excited when they see the "grooming matt", but once we start they calm down and stand still. It's kind of like a different sort of training where instead of being rewarded for activity they are being rewarded for calmness and stillness.
From there it might be easier to work on Brody's nails.
That was my experience anyway. I don't know if it will help with Brody since he really does have issues with his feet. But I do understand the pain of long sharp nails. It was such a relief once Lewis' were done, it was so noticable and I no longer got scratched