In 1970 I did what you are attempting using a different jhp .355 9mm bullet in .38 Spl cases. Pressure will bump up the .355 bullet. I used a 9mm size die to reduce case mouth to provide neck tension and the 9mm expander to flare case mouth slightly. If you lack 9mm dies, experiment by inserting the 9mm bullet into a resized 38 Spl case. If there is sufficient tension to hold bullet in place, run the case into the .38 Spl size die to see if case tension can be increased. If so, you are using this die to taper crimp.
You can achieve velocity goal by using 5 grains of Red Dot. Bum some from a shotgun reloader. I've not used your favorite powder but think it might serve well. In my experiment I used Unique. I had fun.
In the 1960's Lee Jurras of Super-Vel fame put high velocity lightweight handgun bullets on the map. To reduce pressure, he used smaller diameter bullets such as .355 in .38 Spl. The big ammo companies forced him out of business by convincing suppliers not to sell him components.