A wobble on the Morgan IFS can be caused by so many different factors , the tyres are the most obvious and a higher pressure will reduce this.
Once you have confirmed the geometry is correct , equal and you have got as much negative camber as the system will allow (if adjustable) then start increasing the front tyre pressure. When on road tyres in my +4 (with a heavy TR engine so not really comparable) I used to race on 38 psi front , and 36 psi rear. I don't recommend going that far on the road unless you have a very friendly dentist, but definitely go up in 2 psi increments on both front and rear until you find "the sweet spot" (grip v ride comfort) and then try adjusting the differential. I still stand by a 2 psi positive delta in the fronts , BUT your driving style may be completely different to mine.
I agree with K that 20 psi is too low for "spirited" driving , I am guessing it will be in the 26 to 28 range. At 22 psi the tyre walls will distort badly with high cornering forces.
The stub axle itself actually distorts under hard cornering , and this is especially the case with slicks and competition tyres where the grip available at the contact patch is greater than the force needed to "bend" the spindle. This is an extreme example and not likely to be encountered on public roads.
