We have Hebs which are thought of as late developers. We bought a May born tup lamb this year, but then decided to use him on a handful of ewes. We are also using two other tups on small groups - good for genetic diversity to use several tups.
We put the ewes with the tups yesterday; this morning the lamb had jumped in with the senior tup and was chasing his ewes round. Little devil! We have moved the non-breeding ewes overnight, in case he gets them in his sights too, but we will have to put an electric strand right around the lamb's field to keep him away from all the ewes.
So yes, your Herdwicks should be perfectly capable of serving ewes, but bj_cardiff's suggestion of using two together, if it's not for pedigree lambs, would be a good idea. Check their testes and penises thoroughly before they go in to make sure everything is in the right place and healthy.
What are the symptoms of your ram's bad back? Sometimes if a sheep has two bad feet they stand and walk very awkwardly which could hint at back pain but is feet. Or is it a back injury the vet has diagnosed?
The lambs meat should be fine once they have calmed down ie their lower bellies stop being fiery red. We send all our tups which are destined for the pot in August at 16 months, when they are very quiet and chubby from spring and summer grass. Do herdies go then too? They should be fine for meat by then.