I am wondering how many miles have been covered so far, and if the steering has been set up properly for your particular Morgan.
If it's set up well, and properly greased (sliding pillars not too tightly fixed within their bushes), there is self centering - albeit not overly so. The point being that a Morgan is a beautifully set up design which takes a while to be fully appreciated.
Personally speaking the first impressions I remember having of my 4/4 were not A1 at first. Because of misalignment (excess toe in), worn sliding pillars due to poor care, wheels not balanced etc.
Not every garage mechanic is up to speed on these machines and mine came with a complete "service history", (supposedly) undertaken by a major morgan agent and having only covered 7k miles.
I suggest a carefull overhaul and appraisal of the existing steering geometry before tampering with the steering geometry. Only then, try to get at least ten thousand miles on the clock before passing judgement. It takes that long to become self attuned to the characteristics of the traditional Morgan.
Because so many under-use their Morgan, only the few who do put them to regular use become truly familiarized
