That's exactly it. Too many variables at play to colour match consistently. Your best bet would be to sweet talk them into matching manually.
RGB is essentially for screen viewing, CMYK specifically is for printing. So it's not really a matter of making one or the other work, they kind of work hand in hand. Industry standard is anything being sent for print will be in the CMYK colour format. Good article about it
https://www.xrite.com/blog/additive-subtractive-color-models
You will be mostly fine matching a font to the base colour. Even if you are a little off the white in between will be enough to trick the eye. That said, the simple fact is even if you know EXACTLY what colour you need, sometimes the CMYK gamut cannot reproduce it exactly. Dayglo Green is an example of that below. I could go on and on about it, but basically to get 90% of the way there isn't that hard, to get to 100% is where you really spend your time.
Those disclaimers aside:
Colour | CMYK | RGB |
---|
Dayglo Pink | 0, 83, 5, 0 | 244, 81, 151 |
Retro Blue | 99, 85, 36, 27 | 28, 53, 94 |
Mandarin Red | 23, 100, 88, 15 | 170, 24, 44 |
Dayglo Green* | 64, 0, 76, 0 | 76, 206, 113 |
Retro Lavender | 35, 71, 25, 1 | 170, 99, 137 |
* Out of gamut warning - unlikely to match accurately