All very interesting.
Assuming the groat is on a smaller flan of 21mm relative to a sixpence at 25mm and looking at the pics I would say the sixpence has used the same head and crown punches as those used on the groat, but not the shoulders/chest. I couldn't find a coin in Brooker, Schneider or elsewhere which used this style of shoulder punch, but with the caveat that it could be damaged given the lack of V shaped drapery. I also don't know when or whether the sixpences used a complete crown/head/chest punch. These were introduced on the shillings starting with Sharp E3/2 (tun), but it doesn't necessarily follow that the 6d punches were also a single piece from that date - could be earlier, later or never.
Assuming I have interpreted this correctly, that would suggest they were short of 6d punches at the Tower in late 1645, resorting to making up a bust from obsolete part punches and also leaves open the possibility of a pure Eye 6d with this bust surfacing at some point.
More research required.