I don't think you can count on it coming through the new paint in an even an acceptable manner. You've gotta cover it up, and it might take a lot of coats but there really isn't an alternative.

I don't suppose you could tone it down with a white (or something bland) accent wall or two and just have less of the Kraft?

Thinking of primer as necessary to cover existing color is incorrect.

Primer doesn't cover up color. Primer goes on 'sketchy' because it's primer and not a final coat. Many people think a coat of primer is supposed to be totally opaque, solid, and even. That's not how primer works nor is it what it is for.

Tinted/gray primer creates an ideal substrate for the NEW color.

If you need a tinted/gray primer for the new paint color, you're going to need it no matter what the existing color happens to be.

If the color you've chosen does not require a tinted/gray primer, then it's going to cover with the same opacity whatever color is on the walls - doesn't matter if it's off white or sunshine yellow. Coverage will be the same provided it's applied at the appropriate thickness and the recommended two full coats are applied.

Changing your mind about a color after the walls have been professionally prepped is actually no big deal. Might have to pay to apply two additional coats but you've already paid for the prep. All the hard work has been done.

If you don't like the color that went up, now is the perfect time to change it. It's like ripping off a band aid. Just do it and get it over with and once it's done, you'll feel better.

I know they aren't as popular now, but have you considered a faux finish? I had an old bedroom with deep blue color on the walls that I tired of, so I got a wall paper border and put it up after I did a faux finish on the upper portion. It really changed the appearance of the room, and the blue became bright and fresh again.

You may be able to just add a single color on top to change the whole impression of the wall color. For best effect, you can try for a subtle color change...the ones pictured in the link below are much more stark and you need not go that far. You then may be able to just tone down the color you have to get the color you want.

Here is a link that might be useful: Color washing

Always most informative, funcolors.

So can you answer this one for me?
I have usually found that yellow is particularly transparent, and often requires more than two coats to cover well, and to arrive at the correct color. Is this no longer true of newer paints?

Yellow can be very transparent. As transparent as a cranberry, blue-red. Transparent colors require the proper undercoat and perhaps an extra coat beyond the typical two.

Price point is very important when choosing certain colors like transparent yellows and reds. Cheaper paints, even with the proper color undercoat, can take anywhere from 3 to as many as 7 coats. And no guarantee that even after 6 or 7 it's going to look "right".

Definitely want to purchase upper tier paints when choosing certain colors. Because it will save you tons of time and a chunk of money in the long run. The newer paint brews, like Aura from Benjamin Moore, do indeed offer high opacity, more efficient coverage even with the transparent colors.

Great. Thank you, funcolors.

I've also found reds to be a bear to get right, and loved the way the Aura colors perform. We did our den in an Aura terra cotta, and it covered pale yellow-beige in one application, with overlapping roller tracks.

So I would second the recommendation that you use high-quality paint. You will end up using much less, and in a large space you often spend no more than you'd have to for cheaper paint and more coats...with a far better result, and less of the painter's time to pay for.