I have experienced the same issue with a remote filter on a piston ported kit & in my own current set-up, it seems to get better, the further away the filter can be located. Currently, my DIY foam filter is nestling under the air scoop with a 60 mm flexible tube between the two silicone elbows, one to carb, the other to filter. Very 'Deja vu' of my early Lambretta ownership but I know for a fact that the standard air filter box, & particuarly the bellows, simply cannot cope with the demands of an engine modified to deliver something like twice the OEM performance.
The problem is exasperated by the amount of inlet timing, IMHO, which is difficult to resolve with the Mugello (or Rapido)
On 'the other Forum' you will have it suggested that a drain hole in the elbow/bellows will cure it, but I would only advocate that to be applied if in conjunction with a OWV (One-Way-Valve) & tubing or with a filtered breather located downhill from the carburettor. Just like Innocenti used to do.....
TBH, when I have looked @ the amount of 'flooding' there may be after stopping the engine, @ most there may be a fuel 'mist' on the walls of the elbow, but I guess that may be all it takes to significantly richer up the fuel/air charge to cause the starting issue.
That is probably the next step that I will personally try as such items are so cheap on the auction site that it has to be worth a shot. I reckon a 2 mm OWV would be large & 'sensitive' enough to do the job, if, in fact, it is down to 'flooding'
(I must concede, that despite what may appear as cynicism

my engine will start after loads of kicking over with the fuel off to clear what must be an overcharged mix)
If you do try it yourself, please let us know how you get on.....
