I have had a few bikes that would do a tank slapper and one that was successful in pitching my azz off the bike and what I have developed as a means to stop it is this, apply equal parts throttle and rear brake. Keep adding more brake but, keep enough power in it that the weight of the bike doesn't shift toward the front wheel. Using this method I can keep the front end from overpowering me and yet decrease my speed to the point where the wobble will stop. I have used this on BMW's and Honda's and Harley's and have been able to get the bike back under control. Can't say it will work every time for every one but, it is what I have taught myself to get rid of a strong head shake.
Any time any bike of mine has done this I immediately start what ever is necessary to fix the wobble or I get rid of the bike. The time that I didn't know what to do was the summer of 1978 and I have the pictures hanging on the wall in the garage of what I looked liked after a 65 mph slide down the highway with no ATTGAT what so ever. Lotta scabs all over every where on that one. Interesting side note on this incident is that I was running a Dunlop Gold Star TT tire on the front of a 750 Honda single cammer and I had a brand new tire and tube leaning against the couch but, the guys called and said cmon man we're going riding and instead of taking the 20 or 30 minutes to spoon the old tire off and the new one on and do a little spin balance on the screw driver trick, I paid the price for that decision.
I no longer take a chance on running any tire that isn't fresh enough to ride safely. The trouble is that it isn't always one thing that contributes to a speed wobble but, can be many single things or more than one thing coupled with something else. From the dialogs that I read on here and the events I have experienced personally it seems that the one biggest factor on the Strom is having a set of slab sided bags and running them up to and beyond a speed that is aerodynamically prudent? My bike has given me a little wiggle one time and it happened when I was in a strong Wyoming cross wind and I was a little over zealous in hammering the throttle. The wiggle never became violent but, I took action as soon as it started and managed to get my speed down and it stopped.
In 2001 I bought a brand new from the dealer BMW K1200 LT and it came with a small stabilizer mounted on the front end to control wobble and yet at about 40 or so if you let go of the bars it would just kinda veer back and forth. It is a topic of conversation on BMW Luxury Touring.com and has been for years.
My DL seems to be fine up to 95 and I generally ride at a speed lower than that so I seem to be ok on the wobble issue but, I think the bags are the culprit in my case since if I take all the bags off and just go ride the bike I have never had any kind of wobble at speeds well over the posted.
IBA # 25074
07' DL 1000
06' Burgman 650