I don't think that's the tyres, our Amphicar is often driven at 70mph plus and it feels stable and precise even on our narrow roads. It was the same with the previous radials, it did wander a bit on bias tyres, but on radials the upper limit is the engine - noise and ultimately valve bounce - not the handling.
Check very carefully tracking, caster and camber and also any play at all in the rear axles makes a huge difference (pinch bolt area) - it causes the car to sort of steer from the back, many Amphicars are like that.
Cameron hit it right on, with Radials and tubeless tires(Canadian) you MUST use the tire company's specs.
30- 35 lbs..
I have done this for over 20 years on all my cars and ones I work on and all handle good at all speeds if front end is in specs.