You have noticed these very detailed symptoms and that's great - you are obviously a very caring owner. I have not seen anything like this described before. There can be a variety of reasons for partial paralysis - some are 'curable', some are really not, and some are in-between, so piggy might always be a little stiff but can still live a happy life even if he can't do ramps. Yours does sound like a specialist case though, and your currant vet - if they offered euthanasia without knowing what is happening - well, lets just say I would look for another opinion. It makes me really cross. Some vets think 'small furries' are not worth the effort or they assume people are just looking to off-load the responsibility when piggy is sick but they would never say this sort of thing to a dog owner! I mean, I see a generalist vet but if something has been beyond their knowledge or experience they offer to 'refer' me to a specialist.
If you have any way to get to one of the recommended vets please consider it - they are not always expensive specialists - some are just normal vets with normal charges but a lot of experience. You can ring in first and ask about charges for consultations. Ask about seeing a named vet if one is listed - I know at my practice there are some general vets who are much more 'into' piggies and they have the most experience and compassion for our little friends. These are vets that kept/keep guinea pigs themselves and this is also worth asking if you can't find a specialist you can get to.
Piggies going to the vet should at the very least be offered pain relief if the vet thinks there is any chance they are uncomfortable - there is painkiller licensed for guinea pigs which is very commonly given. I am not sure about Osteocare - is this a human vitamin supplement? Did your vet recommend it? We must be careful about what we add to their diet - especially to avoid an excess of calcium. People only absorb the calcium they need from their gut and the rest passes through without problems. As we get older we lose calcium from our bones and older people often supplement the diet with extra calcium. However, Piggies absorb ALL the calcium they eat - even if it is far too much - and then have the problem of getting rid of the excess. They pee it out - but many piggies struggle with calcium stones forming in the kidneys, the bladder and the urethra, blocking their tubes which can be very serious and lead to pain and blood when peeing. Many of us have lost piggies to stones. They have probably evolved to be this way because their teeth are constantly growing and needing calcium. But a good diet (80% hay, 15% veggies and a very few pellets, plus low calcium water which I think you have in Manchester - I remember cups of tea tasting really nice) gives plenty of calcium. Most of us are busy trying to reduce it by limiting pellets and filtering our tap water for them!
It is also just as possible that your current piggy symptoms are completely unrelated to his previous paralysis. 'Clicking' noises as you describe them could be made by his lungs if perhaps he has a lung infection? It makes the breathing noisy sometimes - but I am not a vet remember - he needs a hands-on examination. Head jerking might be in effort to breathe... or it might be something else. If he has an infection the faster you can get him seen the better - there are antibiotics licensed for piggies too. Has your poor lad lost any weight? It is a good idea to start monitoring it (kitchen scales are fine but weigh on the floor in case he tries to leap out!) and keep an eye on his pee and poop output to make sure that is healthy too. A piggy that is struggling with an infection or other illness, that has lost weight and condition, these piggies can also wobble as they walk because they are weak.
Good luck getting to that vet - we will be thinking about you x