I don't know how the shielding would be affected by adding some tin and antimony to the mix. You may want to try wood drills?
If it makes it more machining-friendly, then sure, the heavy lead content would work, if the aim was only to stop the radiation getting through the shield into where it was not wanted. This shield has also not to contaminate space with signatures of metals in the lead.
Here the attempt is to get the radiation to identify metals, and that needs that "quiet zone" shielded by lead. We know the energy is not high enough to provoke anything from the main signature for lead itself, other than a couple of recognizable low energy markers.
If we mix other stuff in the lead, it introduces atoms that will respond, so making signals competing with the responses from the alloys we are trying to identify. At least with pure lead, when the energy enters it, it pretty much gets stopped, absorbed, and turned into (a tiny amount) of heat.
If the shape can't be turned, then maybe we should go for a little casting.
As
@Bi11Hudson has suggested, the idea of a casting that we can hand-ream to finish up seems to have potential.