I'll make a somewhat different suggestion...
You say that 350 and 405 gr. commercial bullets group well with both Unique and with 55 grs. of Swiss BP.
What is the hardness of the commercial bullets?
Why not cast the same hardness of lead using your Lee mould? If it works with the commercial bullets it should work with your Lee bullets. Of course you should size to same diameter as well and if your mould is the HB mould that may make a difference but with harder alloy the HB likely wouldn't expand much if any. I am assuming the commercial bullets are flat base?
Anyway, I'd start by trying an alloy of same hardness as the commercial bullets since they seem to work with both Unique and BP.
If that doesn't solve it then there are lots of good suggestions above.
Longbow