My Morgan was reupholstered a few years back by a local guy who had served his time in an old fashioned car retrimming business and he certainly made a super job of it.
The only bit of the Morgan trim he didn't like was the internal padding along the inside of the chassis frame under the door. In my case it had become damp/waterlogged so needed to be replaced with a waterproof foamy material.
.......and replace all holding down bolts/screws/eyelets for the trim panels, wooden seat supports, etc with SS. I used galvanised to bolt through to the underside and they rusted up in quite a short time. Similarly all tacks need to be corrosion proof.
..........and take your time, each hide tends to be "unique" so you can't go back for an extra bit.
simon