As I mentioned, there is no explicit policy prohibiting strobes in carry-on. Calling ahead will likely do little good, as the TSA gate agent has the final word. If you call the TSA, they will say it's not on the prohibited list. You won't know who the gate agent will be, so you cannot call him.
It might work to call the TSA Customer Service Rep at the airport you are flying from, and get him to acknowledge there is no problem with the strobes. Then, if there is a problem at the security gate, reference your call, and who you talked to. Even then, the agent at the security gate has the final word. If you have connecting flights, your problem is compounded.
In contrast to your problem, I have a Nikon D2x and the oversized Subal housing for it. My carry-on has the camera, lens, housing, 2 strobes, all the arms and clamps, 2 laptop computers, dive computers, plus about 50 batteries AA and larger, and another box of all the other weird batteries I'm dependent upon. I do a couple of international trips each year, and most of the time they don't even look in the carry-on. Never has anyone questioned the items I'm carrying, except for the incident with the stainless steel plates.
I still think it's best to call the TSA airport rep now and relay the encounter, mentioning that the strobes are too expensive and delicate to put in checked luggage. Then ask how to best avoid such problems in the future, and mention that perhaps some of the TSA agents are simply misinformed. Pointless to argue, as they just become more resolute. Like trying to argue with cops, it never works.
Unfortunate that this kind of thing happens, just upsets people and gives the TSA a bad name, all for no reason.