Motocarb of Liverpool sell the carbs and include a selection of jets. If he has supplied one for an MZ he will probably know jet sizes. My Jawa was the first so the jet sizes were a bit of a guess but it worked out just fine.
I always suspected that the shunting on over-run was a mixture of a weak ignition system and having the carb stop too high.
I fitted an ETZ alternator into an ES250 and the tick-over/starting and general running were much improved. I also had a supa5 with a power dynamo ignition and that didn’t hunt on over-run. The ETZ alternator was cheaper as I had one and didi my own machining but the power dynamo set-up is very good, probably around £300 now though.
Motocarb number is 0151 924 5383 and the boss is Steve.
Hope that helps.