Too rich

Specific to the issue:  Keep it simple and rational.  Don't make a "Mountain outta a Mole-Hill" by F'n around with Main-needle heights or Jetting,"plugging this" of "sealing that"  or other obscure ideas.   These suggestions frustrate the shit outta me because they indicate a  lack of knowledge about how the various carb. parts work; both as individual systems as well as in harmony with the other components. Unless you enjoy a good "goose chase".

The problem exists in all 3 carbs so it logical to to focus solely on the "choke" system. The High Speed needle/jet has nothing to do with anything !  It's a completely separate system that does not come into play until higher RPMs require it; as kawboy mentioned.

The Choke Fuel Pick-up tube:  The metering-jet in the end of the tube is pressed in and I have seen many many carbs that have a cracked/split tube  from the "stress of the press" !   I've seen tubes that are 'cracked half-way up their length and the crack is not always immediately evident due to the patena of the brass and or Fuel varnish.  Until you've determined this don't go "J.B".ing anything ! 
There's a practical solution, if required.

By the description of the problem, the culprit(s) would be related to the the "Choke Rod", and/or the Lifting Forks,  and/or the "Choke Plungers" and/or the Choke-plunger seat (at the bottom of the Plunger bore") .
The lifting-fork arms should NOT be squeezing the "Spools". The only contact the Arms should have is when Lifting the Choke Plunger and that should only be on the Spool flange. When the Choke is OFF, the Spools should turn/spin freely and the lifter arms should be midway on the spool.  Not touching the spool, at all !   Otherwise you'll have resistance to closing. 
These Plunger seals are questionable;
 
 
 
 
Lifting forks with adequate spacing to Spool:

 
 
Ensure the choke lever has full travel up and down but specifically down (Closed)  The Spools should also spin freely and move up/down freely on the plunger shaft ( about 2mm). When the plungers are in the Closed position the Lifting forks should not be in contact with the Spools !
Misaligned lifters can create a closing issue.  NOTE:  There is NO up/down orientation.  They are made symmetrical.  The misalignment can be from an asymmetrical point on the screw and/or the Point of the screw finding its "home" in a previous dimple in the choke-rod.  The "arms' on these lifting forks can be bent to the correct position very easily as the material is fairly soft.
 
 
If the Seat (in the bottom of the plunger well)  has any nicks/dings there will likely be leaking.  All 3 at the same time, you may ask ?   "If you think it could happen then it probably can and likely will" , so don't discount the anomaly.