And you are right: The ATN20 does fit, I had to give it (reluctantly) a strong push/pressure and it clicked in (see last photo)Hmmm, strange... Shall mean: That the ATN14 wouldn't properly fit onto a Signet TK1E to TK7SU family was just what I expected - but I'm really surprised, that the ATN20 wouln't fit.
If it's not too much work for you, could I ask you for a side-by-side side view pic as well as a side-by-side bottom view pic of your AT20SLa and TK7E bodies, both pics without needle - and also a side-by-side top side (or respectively inside) view pic of your ATN20 and TKN2?
The side of the plastic though doesn't fit as it would be perfect. There is a small (air-)gap