Just not going to happen without a tinted primer. Except it and move on to the next job.
I've seen customers on there 7th coat of paint when trying to do this without the tinted primer I had not only suggested but had bought for them and had on site. http://www.house-painting-info.com/tinted-primer.html
It does seem counterintuitive, doesn't it Red? I've had a few difficult times over the years trying to explain to customers why it might take four or five coats of a dark color. I've also been pressing the paint cos to put an explanation in writing for just that educational purpose.
Some colors may require as much as 16 oz's of tint, and that's a lot when you consider that a few drops of red could simulate a crime scene. In order to fit that much in a can they must remove other things, and one of those things is white titanium dioxide. What is removed is what gives the paint "hide", tint does not give hide. Some deeper bases are called clear bases, and have no color at all. That's it basically.
As to gray primer, I don't believe that works, at least not in my experience. I did a front door in a deep cranberry color. The paint store gave me a gray primer calculated by the computer for my finish color. Well, after four coats of finish on top of the gray I called it done. A fifth coat would have given me the depth of color I wanted. That experience was not an isolated incident either.
I use Ben Moore anymore, almost exclusively. Because of their new technology their dark colors almost always cover in two, even over white. That's what they claim, and it's proven to be the case.
I have used some shades of red that would damn near cover white in one coat and some that would barely cover it in 5 coats. I use tinted primers over light colors because it does help with some brighter reds.Always buy a premium paint.
JS I have found instead of tinting the primer gray for these colors I just buy glidden "gripper" i think its called. Its already gray, this has worked pretty well for me. When just tinted I ran into the problems you had. I have not tried the BM deep colors yet.
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