Dr. Smoke,
I have done a total of two veneer refurbishments on two separate Healeys I've owned (unfortunately, my first Healey was claimed by "Sandy" back in 2012). However, on both Healeys, I've utilized a two part epoxy resin, although the first Healey was done as a "pour in place" approach with no cutting down the epoxy (ie., sanding, compounding and buffing).
My second Healey, which I still own and enjoy, also utilized the two part epoxy resin approach, but this time, after pouring and letting it set (cure), I cut down the thickness by using various grades of sandpaper and compounds, then buffing, proving to be a much better and 'professional' looking finish. Healey Nuts mentioning of the epoxy resin approach as mentioned above is, I believe, the same or similar what I had used.
In addition to my preparing my second fascia refurbishment, I also had to resolve issues I had with 'checking' or peeling away of the existing wood veneer from the wood substrate). On that plus the application process, I posted my approach here on the Forum some years ago. If interested, one can research by typing, Epoxy Resin Dash Refurbishment.
Nonetheless, whatever finish you desire using, it is, in my humble opinion, to do it right and to have control over your finished product, I really see no way around doing this other than completely removing the veneer fascia and laying it flat as possible on a horizontal surface so as to avoid pooling, cascading, etc., of whatever liquid medium used, not to mention how to negotiate around the existing chrome trimming, bezels and so on, if one decides to leave in place.
I suppose it is easier to apply varnish or whatever liquid medium to the veneer used, leaving everything in place. Or, go through the chore of removing everything from the wood veneer (and yes, that does mean removing the oil/temp gauge gingerly along with everything else with all other bits, pieces plus using muscles in your body you never used before)!
But let me say that every time I look at my Healey, the one thing I draw my eyes to is that dash! That says just about everything to me!
Good luck!
Paul