I'm in a similar quandry with a 300wm and 165 cup n core. I've had no success with H4350, so I loaded up to do a ladder test with IMR7828. And I'll let you know the results when I shoot them here in a few days. A few different manuals show 7828 to be a good choice for this combo. Fills up the case really well. Different I know than your ttsx, but the cal and the weight are the same.
One thing I've found with shooting copper, if your barrel was shooting cup n core prior to your switch to copper, make sure you scrub all prior copper traces out of your barrel as the two different copper alloys are 'sticky' to each other and you'll get poor groups and poor velocity. Particularly so with Hammer bullets. FWIW.