IMHO you got it right. The charger is correctly and continually attempting to start the battery but not succeeding, so we know the charger is working. You're getting nothing on the SOC reading, but we know the BMS LED's are working because the SOH also works correctly from the pattern of LEDs that do light.
The SOH shows the battery cells are already half life expired; IIRC Halfords rate the battery for 2 years/500 cycles >60%. Even if you're prepared to open the battery and "bump" any low cell strings (which is the direction Neal is taking), you haven't got a great deal of life left in the cells anyway. The indications seem to be that at least some cells have probably sunk way too low for recovery, but trying that may still be worth a shot.
On the other hand, your half-life cells may be okay or recoverable and it may just be a faulty BMS, but with the BMS being specific/unique to Halfords/Suntour with comms everywhere means you're still screwed in terms of being able to replace that with a generic one.
IMHO I'd say you're flogging a dead horse. For peace of mind, I might be inclined to take both charger and battery into Halfords and ask them to double check by substitution, but beyond that I'd be looking for a new battery or an alternative too.
Just my two cents.