The 276 Type carb originally fitted has a remote float chamber, this can be lowered by additional fibre washers between the float bowl banjo and the mixing chamber body union nut. This will lower the fuel level in relation to the needle jet outlet and is worth a try. From description the fuel level is simply just a bit too high. A missing or too thin sealing washer under the jet block can also raise the level by raising the union nut and float bowl so that fuel overflows the needle jet.
Later Monobloc was a popular conversion back in the day, but as noted, on Plunger bikes it is a tight fit and no room for a filter connection. If you still have the rare and relatively expensive original air box, well worth persevering with the original carb type. Set up properly they work well.
Swarfy.