Thanks for the compliment, but my car looks best only when the picture is shrunk down to the size of a postage stamp!
Adding the cockpit trim may be doable, but your 4A was the first TR with the later style convertible top permanently attached. This required the rear plate to be bolted to the back cowl area so those cockpit trim pieces would either interfere, or always be covered up. If you really want those trim pieces, and aren't trying to be perfectly original you may be better off going with a TR4 top which was removable - and that probably means a new aluminum header for the top of the windshield as well as a set of TR4 hoodsticks for the top.
The trim pieces also used a bunch of screw in lift-the-dot posts, which is really how it attaches to the body - that would mean a TR4 tonneau cover as well to be compatible.
My vote would be stay with the 4A bits on your 4A, and if you really like the cockpit trim get a spare TR4!
Randy