Try dropping your front pressures to 30psi. If that makes no difference then I'd start with the steering damper. That's the bit that looks like a great big bicycle pump. Undo one end and see if you can move it in and out. If it doesn't seriously resist you - replace it.
After that, if you don't know what you're up to, get it into a Landy independent and ask them to get it up in the air and have a good nose around. Then, once you know that it's mechanically sound and it's still not handling correctly you might want to look at replacing the tyres.
The last thing you want to do is throw away perfectly good tyres if you're not as certain that you can be that it's going to cure the fault.