I'm no expert but I think you should get a second opinion ASAP.
Personally I would find somebody suitably qualified to have another look and, if necessary, carry out the dental work without general anaesthetic. You can also contact the CCT to see if they can help (they routinely carry out conscious dental work). I know it's a really long way but people do travel from far & wide to get help from Vedra. If you can't travel to Cambridge then she may be able to point you in the direction of somebody nearer to you who could help (especially useful if it requires regular treatment).
Perhaps you could contact any guinea pig rescues in your area and ask if they know of someone local who is suitably qualified to help?
As I understand it, if the teeth are a problem then that can definitely cause pain and a sore mouth, due to rubbing. He's bound to find eating difficult if he has a sore mouth and pain can also affect the appetite anyway. It sounds like perhaps he wants to eat but can't, rather than simply losing his appetite...do you think? I believe that some people use Daktarin oral gel to soothe affected areas, in cases like this, but I'm sure someone else can advise for definite.
With regard to the suspected kidney problems, has the Vet actually properly diagnosed this yet? I could be way off but even something like mites can cause guinea pigs to become very irritable when being touched around their lower back/back end. It may well be that he does have something serious going on but if you're not confident that your Vet is doing his best for Louis then I'd honestly look for a new one.
Btw which antibiotics is he on, what's the dosage and how long is the course? Has he been given any other medication at all, like an anti-inflammatory or painkiller? As I said, I'm no expert but I'm sure someone more knowledgeable will be along in the morning, if not before.
Good luck. I really hope you get the help you both deserve x