Hi Deggsy, sorry to be the bearer of potentially bad news, but I suspect that your new adaptors are for Spitfire 13" wheels only.
The splines on 14" and 15" wires are the same regardless of the rim width as the centres are interchangeable (some have more/less spokes but the hub is the same width), but the Dunlop 13" wheels fitted to the Spit/Herald/Vitesse/GT6 have a narrower central hub. If you trial fit a larger wheel to your new adaptor I believe you'll find that the threaded portion won't extend out of the wheel centre so you can't fit the spinner.
The 13" adaptors do tend to be cheaper at about 2/3rds the price of the larger ones, and that almost caught me out when I built my Spyder.
I'm struggling to find an article that details the difference, but read the info on this ebay listing -
https://www.ebay.co.uk/itm/Triumph-S...-/383101263911
Hope you're able to sort it and fit the wheels you want.