This is what I have so far.
200 gr Sierra 51.0 gr IMR 4895 1 1/8" @ 100yds.
220 gr Hornady51.0 gr IMR 4895 1 1/2" @ 100yds.
220 gr " 39.0 gr H 4198 1.0" @ 100yds.
235 gr Speer 50.0 gr IMR 4895 1 1/2" @ 100 yds.

I've started trying some cast boolit loads.
MUCH MORE ECONOMICAL

250 gr Lee # 375-250RF,
Wheel weights,
sized to .377
45.0 gr IMR4895 with dacron filler Vel 2249
( way too fast!) 6" group!

Will try this again with 32.0 gr.
Looking for a vel of around 1600FPS. Should be much more accurate too.

Same cast boolit with 40.0 gr IMR 4198 & dacron filler Vel 2315.

Also way too fast & 5" group. Will drop this load to 30gr & retry.

Will post results here.

BTW the barrel on that Handirifle is 24"

Which barrel did you start out with?

This one. I started out with a .375 blank.

Great stock. Did you make that one yourself? That sures takes the Handi to a new level. Is your barrel made on a stub? That is one slick idea.

Yep I carved the stock & forend from the same chunk of black walnut. The stubbing sections are the middle photo. The stub was made from a 12 gauge barrel & the barrel is from a .375 contoured Shilen blank.

FWIW: My experience with the .375 JDJ has been limited to the 14" Contender so I don't know how well this will translate to your (very cool) rifle, but here goes:
Some of my best results with a jacketed bullet for medium game:
40.0 gn IMR4198 behind a 235gn Speer semi-spitzer.
With the 245 cast:
30.0 IMR4198 for practice loads.

Thanks for that info Don. I forgot to include my latest load for my 375 in my original post.

255 gr Barnes original
48.0 gr H4895
Avg (5 shot) vel 2,347fps
3/4" 100 yd group

This is my go-to hunting load. Not a cheap bullet to shoot. Thats why I am going the cast boolit route for plinking.

I have some 250 gr cast loads loaded right now with your load of 4198. Just waiting for the rain to stop so I can go shoot. Will post results here.

My experience is also with the 14" Contender. AA2520 has been a good powder in my barrel, with Hornady 220FP, 270SP, and the 300FMJ all hitting in the same group at 100 yards.