God bless eBay. I find it a right pain having to buy the odd tool for the odd/rare job. I guess there's no other way. Similarly, for "DIY" there's a few on my street in a similar position, so we have a bit of a community tool box... Works fairly well. Ride safe.
my 12,000 mile service is due later this year, and got to check what parts of the service the mechanic I’m using is going to do. I’m happy to do the linkage bearings and head bearing myself if I don’t need to spend much to be able to do it, compared to a few hours labour paying for it to be done.
What year is your bike? My 2015 has a hex outer (but would likely get marked) but also has 6 round pin holes, if the same surely you would be better with a socket that has round pins? e.g. this?
Try Turbosuzukis he sells on eBay etc he makes these for £25 ish he’s a top bloke I’ve had a few off him for different bikes.