Sounds like the very opposite of my car and despite having electric PAS, doubt that makes much difference at speed. Also a heavier car with small 13" wheel so likely you have a steering geometry issue.
Don't think higher tyre pressures is the way to go BTW. The recommended 22 psi takes account of the cars lightness and the fact they are an important part of suspension (read comfort).
As a start I would find a shop that offers laser tracking and have them adjust for minimal toe in. The book suggests 0 to 3.2mm (⅛") total - wonder if you have too much?
