Your bike has almost zero trail, which is most of the problem. Flipping the forks so the axle is in a trailing position should give you a decent increase on positive trail, because I am fairly certain your setup as it sits right now has zero or near zero trail. Combine that with a very rear heavy machine and it's not too surprising you have a wobble issue. You have a front fork setup that wants nothing more than to turn itself around in motion, and then almost no weight on the front tire.
Would you be able to provide me a full on broadside picture of the bike with the front wheel in line with the frame? Specifically a picture with a good view of the front suspension setup. Include something for scale, such as a drink can or other well known object.
(Edited my comment because I realized my 5AM morning brain typed something my 7am brain wouldn't have)
