I would get some sludge remover from a plumbers merchant or screwfix etc. Sentinel X400 or similar, add it to the feed and expansion tank and leave in for a week or two and then drain down, if it's only mild sludge build up then this will do, if its excessive then I suggest a proper power flush. After you're happy I would go ahead and balance the system, you could balance first and then add sludge remover, this added circulation might shift the sludge around but it's quite dense and usually doesn't budge too much if excessive.
PS. Sorry I didn't fathom out what you were getting at sooner. From your description I was picturing the bypass gate valve as a cold feed valve to system.
PS. Sorry I didn't fathom out what you were getting at sooner. From your description I was picturing the bypass gate valve as a cold feed valve to system.