Potts,
All great advice and comment above especially Lorne in that they all drive differently and need fettling as per the car and drivers preferences!
Tyre's, well you'd be surprised how they will effect the drive. If you are sitting on the tyre's the car has for all that storage time they will be crap! regardless of what they look like! Fortunately they are fairly cheap tyres!
Where are you based, Its possibly time to get an experienced morganeer to drive, assess and look at the car. If this is your first experience of Morgan driving all I can say is they drive very differently to a modern car, actually in a lot of ways better! as its all about driver and car.
A driver used to them will know whether its driving correctly or not, or what is not working and probably how to start to correct any issues.
It really isn't about guessing what might help or listening to some who will confidently tell you " ah you need this doing" Firstly the car has to drive like a Morgan and then you can start to think how you want it to drive!