I have tried to think of alternative methods of capturing the sheep, but in the situation you present I really can't think of anything. In our own situations and with the animal husbandry knowledge that I and other TAS members have, we know how we would deal with these sheep, but you are in your own situation and those methods just would not work for you. I know for a fact that just chasing Soays from place to place will not end in their capture. Soays can be run down, eventually, as they have a natural tendency to 'go to ground' when they are exhausted, but it doesn't sound as if you have the fitness to do that, and anyway, it's not exactly good for the sheep either. It sounds as if your neighbours are all fed up with them, and perhaps with you too. As you realise now, you went into this situation without understanding what you were letting yourself in for, or an understanding of your responsibilities with regards to your livestock and your neighbours.
Soay sheep are notoriously hard to round up - they are simply not like other sheep which flock together; Soays tend to scatter before a dog or flapping humans, as you know. It's not their fault, it's an innate response to being prey animals. 'Normal' sheep flock together for safety in numbers, Soays scatter and run for the hills. A sheep dog not used to Soays could be totally confused by their behaviour and unable to cope.
If one of your neighbours was sympathetic then the sheep could be contained with their flock in a field, and brought in at one of their routine gathers, separated out and returned to you, with some financial recompense for their care and feeding of your stock. But would that situation sort the problem? There is still the fencing you would have to Soay-proof and you would have to have in place some kind of handling system to manage your animals for normal husbandry tasks such as foot trimming/checking, anti-fly strike spraying, possibly worming, roo'ing/shearing and just generally doing health and welfare checks. It sounds as if you are unequiped for those tasks so are unprepared for the return of the animals.
You say you emailed the RSPCA and have had no result. Well, phone them and speak to someone who knows what they are on about. Think beforehand just what help you need which I would think would be for someone who has experience of catching wild animals to catch them then take them into care for their wellbeing (which is the only reason the RSPCA might accept - they certainly wouldn't do it just to return them to you into the same situation). I detect a bit of an attitude of expecting others to help you, but you must realise that these sheep are totally your responsibility, and act accordingly. Clearly none of your neighbours has any more of a clue about how to handle Soays than you do, and why would they? So I think you are down to a choice between getting help for the sheep from the RSPCA, or getting someone to shoot them, as suggested by several of us here. Giving adequate care to your domestic animals is governed by law, so you can't just abandon them wihout some sort of comeback on you. This is not a situation where you can just let things drift anymore. As Anke has so wisely pointed out, the sheep could wander on the road and be the cause of a fatal accident. You have to make a decision pronto.