Rabbits most certainly can have teeth removed if it's necessary. It can be difficult because rabbits have teeth that continue to grow and it can be difficult to get the teeth extracted so that they don't regrow, but surgical extraction is done in certain circumstances, and certainly in the case if there is a rotten tooth or loose tooth that need removal. Though with the age of your rabbit, that extensive of a surgery if it's really needed, could be risky, more so than a regular dental trim.
http://www.medirabbit.com/EN/Dental_diseases/Differential/Rabbit_dentistry.pdfhttp://www.medirabbit.com/EN/Dental_diseases/Rabbit_dentistry1.pdf
I can't see how weekly injections of depocillin are going to be enough. Depocillin is pen g procaine, which is a short acting penicillin. Meaning that it doesn't reside in the system long, therefore needs to be given often, usually daily. Even Varga's(UK rabbit specialist) Textbook of Rabbit Medicine lists the dosage as daily, and Varga is a UK specialist that worked with Frances Harcourt Brown, who originally wrote the Textbook of Rabbit Medicine and is pretty much considered the expert on rabbits in the UK(and possibly worldwide), particularly in dentistry.
http://wabbitwiki.com/wiki/Common_drug_dosages_for_rabbits
The pen g that is long acting is called pen g benzathine. The protocol that I have read for treating head abscesses in rabbits with pen g, is using a combi pen g, that has both pen g procaine and pen g benzathine. I would ask your vet about it and maybe show them the article that I've provided a link to, and see what they say.
http://www.bio.miami.edu/hare/jawab...n Effective,acidic environment of the stomach.
http://people.umass.edu/~jwmoore/bicillin/bicillin.htm
If going with the depocillin, I wouldn't want to do anything less than daily injections of the depocillin, and this would be long term, several weeks at least and that might be a bit of a pain to have to do every day. So if you can't get the combination pen g procaine/benzathine long acting pen g that can be given every 2-3 days, you may want to consider a different antibiotic that can be given orally instead.
I've found oral azithromycin(suspension), to be quite effective treating head infections in rabbits. Though keep in mind that there are a few rabbits that respond very negatively to it where it causes severe digestive upset. But so far for the rabbits I've had to use it with, the most it's caused is some stomach cramping for the first few days. So if you can't get the long acting pen g, or you would prefer to use an oral antibiotic over injectable, maybe ask your vet about trying azithromycin.
With your vet saying that rabbits can't have their teeth removed and recommending weekly instead of daily depocillin injections, I'm inclined to think they aren't terribly rabbit knowledgeable. I know the vet issues you've had though. If you think you may need to go to a more knowledgeable rabbit vet for this, I believe the closest to you might be Sarah Pellet at Animates in Thurlby, but I don't recall if that is where you were going previously or not. There's also Simon Maddock at the Cat and Rabbit clinic in Northhampton, that I've seen recommended by other rabbit owners there. Then there are Iain Cope in Newmarket, Marie Kubiak in Stourbridge, Manor vets in Birmingham(not sure who the rabbit vet is there), but those would be a bit of a drive. Or you could ask your current vet to consult with a knowledgeable rabbit vet or specialist like Varga, Cope, Chitty, etc. That might be the easiest option.
