I can admit to having a very similar experience to the thread starter, in a similarly lowly powered PA38, operating at that time from Liverpool with 2 POB. Lovely warm day, little if any breeze. Intersected take off after nothing heavier than a Shorts 360.
We were airborne by about 12 feet and then had almighty wing drop, one way then the other. How we never hit the deck again I can only imagine. My "passenger" was my instructor for the day and I was still a student.
Analysis of the near incident led me to believe that even the 2 minutes we had were inadequate, and that we were caught as much by residual prop wash as from the vortices generated upon the rotation of the previous aircraft.
You made the right decision to get into the air. That way you are flying in the parcel of air, despite what the air itself was doing.