Fuel dripping from air filter

Your Float Needle Valve is not sealing.
The float chamber is overflowing out the main jet into the carb throat and out the Air filter.

If the engine sits Prop End Low (Pusher?), fuel may also flow towards the cylinders.
If so, also be cautious of a hydraulic lock and/or fuel in the Oil.

The carb vents will only overflow if the leakage is massive.

Just my thought, but is your answer in the picture you posted?

Edit: https://www.rotax-owner.com/en/912-914-technical-questions/3781-excessive-fuel-pressure-revisited

I'm with Bill. Either the float needle is leaking or the float armatures aren't adjusted correctly. To rule out any of this you need to take them back off and make sure you have the needle in place correctly and remeasure your float armature height.

I just had a gentleman come to me that had just rebuilt his carbs and his leaked the same way. Found 1-2 small items, but the offender was the float arms were improperly measured which allowed way too much fuel into the bowls and it came out the air filters on both carbs.

You can wonder for a week and try other things, but until you rule out the above which is one of the most common causes it will be a stone left  un-turned and not ruled in or out.

Hi Justin

I note you put on a new fuel pump.  If by chance you were updated from the old AC pump to aluminum body Corona pump it should be noted that they run at a higher pressure.  The older versions (metal body) ran at .4 bar and the newer runs at .5 bar.  As pointed out if the needle valve to seat is worn or if the level is too high then that is your most likely issue.  Be sure to check out what Bill and Roger have pointed out.  6.6 PSI is less than the max that the new pump produces so that is not out of line.  

Cheers

I am on my third new style pump and they all have put out a higher pressure initially and then then pressure always dropped back to about 3.75 PSI, maybe it has to due with some form of a break-in process.