In my rechambered martini (it has worn rifling and pitted bore);
I have settled on the 35 gr. Hornady Vmax, 11.8 gr. Lil Gun and CCI 500 (small pistol) primers. I get about 3100 fps and on a good day, about 5/8" groups at 50 yards.
All the older martinis have a 0.223 inch groove diameter. I would not worry about using 0.224 size bullets in your martini. Just do not try to overload your rounds. If you want more power, get a rifle in 223 Remington.
Also remember, the martini has 1 in 16" twist, meant for the 22 LR. A long-in-length bullet will not stabilize too well with a slow twist. I have tried 40 gr. Hornady Vmax (quite long with its boattail and polymer tip) and got large groups at 50 yards. I can not remember if there was any yawing. I did not try any heavier bullets as the research indicated poor groups and low velocity for heavier bullets.
I have tried 40 gr. Sierra flat base soft point bullets meant for the 22 hornet (0.223 diameter) but the groups were poor, about 1" to 1.5" at 50 yds. I think the reason the bullets did not do well was the rifling was quite worn, in fact was gone in the first 3 inches in front of the chamber. The bullets skidded through the bore. As a result, I tried the 0.224" 35 gr. Vmax. The results was so good and I was getting tired of experimenting any further, so I stopped.
I hope this helps.