I've had friends use the specialised damping thingies and they seem pretty happy with them - but that's on 22mm skinny tyres riding 180km in the alps. If you've got fatter rubber on the tricross I'm not sure how much difference you'd notice. Most carbon forks are quite comfortable anyhow - compared to say aluminimum - and I've not ridden steel rigid forks for a long time now. Since I'm interested in buying your kinesis forks, I'm happy for you to have changed them anyway (or did you want to sell the specialized forks instead?)
Some people seem to have complained about the tricross forks on larger frames being prone to judder under braking - that seems quite common though on cyclocross bikes with carbon forks, and is due to the steerer flexing under braking that kinda puts the brakes on more while it flexes (this assumes you have cantilever brakes).
Specialised seem to have a part to prevent the judder (
http://cdn.specialized.com/OA_MEDIA/pdf/manuals/IG0226_Tricross_Guide.pdf) which works by suspending the brake cable outer lower down so it isn't affected by the steerer flexing. Also - later tricross seem to have switched to V brakes (mini-V?) which would be unaffected. Seems a common cyclocross choice anyway.
If you don't get the judder, it's not a problem.
If you do and it bothers you - you can adjust the straddle wire height to reduce the effect (I think making it higher helps?), or get the widget from specialised, or switch to V brakes, which are about 12 quid upwards.