Sounds more like the tyres are making the bike feel nervous. I've fast-road-ridden, tracked and raced a number of essesses, and they feel more like a comfortable armchair than anything else
From personal experience:
an oversize rear tyre on an ss that is half worn makes the front feel like it is going to go away from you
an overpressure 60 profile front also feel similar
a side-worn 70 profile front also feels similar
a past-its-sell-by front also feels similar (old hard rubber)
OR !
Front springing - how heavy are you compared to how soft do the springs feel ?