Thank you both so much for your kind read-through, and kinder comments.
But that's merely the fabric. The whole idea is to get it from this point:

To this point - in your own preferred shade and hue, of course:


Here's how I went about finishing mine.
The last layers, the lacquer, were simple enough. I just bought two spray bombs of Mohawk Pre-catalyzed Nitrocellulose Lacquer (Gloss), and emptied them both onto the cabinet - in about five thinly sprayed coats, of course. I may take the sheen off with some 4/0 steel wool (but not just any old 4/0; the kind intended for woodworking and finishing, which has no or very little grease in it). But right now, I love it, just as it is.
And as I've insisted elsewhere,
I'll be damned if the whole cabinet does not sound inexplicably and indescribably better wrapped in the tweed and finished with the shellac and the lacquer.
Leading up to the lacquer:
To the unfinished tweed, I brushed on two coats of Zinnser Universal Sanding Sealer - the exact product is pictured below - following the application and drying times on the product label to the letter;

On top of that, I applied, with a brush, seven thin coats of a beautiful shellac - pictured above! the stuff in the jar - that I solvated and de-waxed myself;
On top of that, I applied, again with a brush, two more coats of the Zinnser Sanding Sealer, to create a "bonding layer", and became very upset by the colour shift caused by the slightly dark sealer;
And finally the lacquer, which weirdly seemed to reverse the sealer's effect on the colour - differing qualities of reflection or refraction between the products? - maybe. Regardless of why it happened - it was a relief!
I so wanted to stop after the seventh layer of shellac. The texture of this stuff is really interesting, like an organic glass ... almost feels alive ... and the colour is incredible, so deep and rich. But, it's not furniture, and needs the protection of the lacquer. Besides, the lacquer might age in an interesting way - especially the really hard pre-catalyzed stuff. It might get some great cracks in it!