How appropriate are the open source licences currently in use for inclusion of HDL cores in a commercial product?
i'm not familiar with all on your list. I see TAPR as analogous to GPL, and good applicability to HDL. others may be tricky. I've wished for a TAPR sort of thing designed for hardware/hdl code that is more like LGPL, but i haven't seen one like that.

GPL, LGPL, BSD etc. are written for copyrighted stuff, and that sortof leaves open a loophole for hardware designs. you don't "publish" an asic, so there can be a breakdown in legalese fitment there. FPGAs may be slightly better fit, as for fpga you do something comparable to compiling spurce code, and distributing the bitfile is a little closer to publishing something you can copyright than doing PnR for a hardwired asic, and you can make your fpga design updatable by downloading and installing new bitfile,  which is like getting and using a lot of software today, but it's still muddy waters for copyright based licensing.

i'm also not sure of cross-compatibility between the copyright licenses and the hardware-specific licenses.

IMHO, of the ones i've read, TAPR is best, but like gpl makes your entire project open-source under TAPR. I's prefer to see cores under an lgpl analog. contribute improvements to the ip core, but protect other parts of the design.

as i understand, the copyright license weirdities are enforcemen
t related. so mostly a problem if you sue a user that didn't follow the intent of the license, they may get off on technicalities.