I’ve solved the wild color differences between screen and print by teaching the client that reflective color (print) and emissive colors (screen) are never going to appear the same. If they do, it’s an accident or illusion.
Pantone swatches are supposed to show the “Real McCoy” but even ink mixing can be botched. Drying time, paper choice, lighting conditions, etc all affect the perception of printed color. For screens, it can have to do with make, model, angle, age, calibration, etc. No two consumer-grade monitors render color the same. No two printers render the same – especially when specifying in Pantone colors.
Clients also need to “see” how RGB, CMYK, and Pantone color space (gamut) overlap but are not the same.
Telling them this stuff is called “stress inoculation.” Reducing surprises. They need to know it’s a crap shoot.
The biggest problem is client expectation. They have to realize, at some point, tweaking the colors isn’t going to make that much difference to someone (the audience) who has never seen the piece before. Nor in the desired results. They have nothing to compare to. The client
becomes biased because they’ve seen the work under different conditions than the final. And “Approved” it!
Color, of course, is important for selling fashion goods and food. Green flesh tones are alien. No one wants to buy green or purple bread.
You can train clients. It takes time and energy. Build that instruction time into your price. I used to do all of my client proofs with printed output. Eventually, I got clients trained to use PDF proofs and to TRUST my judgment. I only use paper now for invoices. :)
Credibility is trustworthiness, expertise, and enthusiasm. That’s what they buy when they hire you.