Raise the tail! Don't land pavement with long taxis!
I had the same when using my tail ski, sometimes it would do it, other times it wouldn't, take the ski off and the issue goes away. The ski must change things back there, not too big of a surprise I suppose, mine was bad enough that I would never put up with it in the warmer months, but I just avoided the issue by taxiing tail up, (Rans S-7S) landing in deep powder is pretty effective also!
This year, due to a new T-3 tail spring, I totally redesigned the way I mount my Datum ski, using a tailwheel dedicated to winter ops, come spring it will all come off as a unit, and my bigger and tougher tail wheel go on. I have not had to taxi on pavement yet so don't know if it will be the same. Ignore that red thing, that's my tail release. It's mass probably won't help, or, who knows it may dampen any shimmy.

Note that now it's more like the mains, limit cables and a bungee. It should make life easier on the attach bracket as now it can conform to whatever comes along.
You may find that you trash your mounting bracket, as you have no give in that ski. My first home made attachment for my ski was similar, no give. As a result, my mount hardware got beat up, things got bent. Here's a pic of my current setup.
