Alliant uses 5.2-5.8 starting to maximum for a Gold Dot which has a plated jacket that is softer than a drawn jacket, but harder than Berry's, so you could probably run the Berry's starting at least to the starting load and maybe all the way to the top, watching for pressure signs and metal fouling and accuracy not getting suddenly wild. This is also assuming you use the same seating depth.
Seating Depth = Nominal Case Length + Bullet Length - COL
If you want to know the COL to target to achieve a particular seating depth you've learned for another bullet then just rearrange the above formula:
Target COL = Nominal Case Length + Bullet Length - Seating Depth
For the TL bullet, since I don't know your alloy hardness, figure to start where you suggested and to work up, using a chronograph, but not likely to exceed 5.2 grains. Again, this assumes same seating depth. Deteriorating accuracy or excessive leading are potential pressure signs, signalling you to back down.
After altering burn rate to get a velocity match with the Gold Dot data at Alliant, for which the seating depth appears to be 0.204", both cast and Ranier plated bullets hit 975 fps (4" barrel, as is standard for 9 mm testing) at 4.7 grains of Unique. So measure your bullet lengths and use the second formula, above, to give you a COL to try. If you have to seat deeper to fit and feed or pass the plunk test, then bring the powder down 0.1 grains for each 0.018" deeper you have to seat to stay at about 975 fps. From the 4" barrel, the pressure is less than 2/3 the Alliant maximum with this 975 fps load, so that simple increase in depth and change in powder charge don't change pressure enough to matter until you go more than about 0.18" deeper in seating depth.
The issue is going to be whether or not this light load will cycle your gun.