You can use the Barnes TMZs in HPH 24 sabots. I have had good success by loading a HPM sub-base under them. I get about 5/8 groups, at 50 yds, with that combo and 120 grs of 777. Buy the way, Buffalo Bullets ships a 375 gr botail spitzer, all lead, and they come in HPM black sabots so they must think a botail will work in them.
I killed two deer with that combo this year and was able to load the second shot without swabbing and it worked fine on the second deer. I didn't get very good accuracy with just the HPH 24 sabots. I don't know what the sub base did, all I know is that it worked in my Omega.
Hope this helps. I use the 290 gr bullet.