Up the rear tyre pressures if they will take it, chunky AT tyres have big tread blocks which move around more. Fit a new anti snaking hitch or an aftermarket anti snaking kit. Worked wonders on my race car transporter

If the load is light in the middle but heavy at both extremes it will have high polar moments of inertia which will encourage snaking. Most weight centred over the axles is ideal, but not easy to achieve with bikes, but obviously it should be nose heavy, I think the P38 will stand 150Kg on the hitch so aim for something like that which I'm sure the classic will stand too.