On pic #1 it is fairly visible even to us that where the icons are placed into their sockets the gold plate has rectangular depressions. And here: >>26989 the "backside" of the Thomas icon is also a fair example. According to Wikipee similar depressions, or rather the outset of them were found by the goldsmiths on the end of the straps.
For us (the general public and not just us here in the thread) it would be nice to see actual photographs of these, sadly the article missing such.
I found an article in scientific journal however by the de facto leader of the Crown Committee (Lovag Zsuzsa) from 1986 where she published several photos of the cross strap pieces, two of them depict the lower parts which are joined to the rim. #2 and #3 this one is upside down are the photos in question. Granted they just black and white and not very good resolution, however we should see the signs of those initial depressions of the icons' sockets. There are none. The only observable unevenness is the result of the riveting process.
For reference #4 is a shot of a strap and the central piece (with the Pantokrator above), the depression is clearly visible on that.
The colored examples (#1 and the Thomas icon referenced above) also show no sign of such depressions tho it can be argued the angle makes it hard to recognize them.
It is possible that only one strap or maybe the two not published in the article - where I found the photos - have that feature, but that would mean only that one or those two had "extensions" and icons on them.
The members of the Crown Committee subscribe(d) to the hypotheses that say originally the cross straps contained the icons of all twelve apostles whatever it was (crown, relic holder etc.) before it was assembled with the rim, so maybe it was a wishful thinking on their part when they believed they saw those depressions, when they mistook random deformations with them. It was the verification of their own ideas so maybe they read more into them than they should had.
Or maybe the author of that article is in some monkey business - since the original reports can't be easily accessed. (In case a Hungarian reads this and has access to them: please share!)