You can rock this on a 6co manual. You'll need to sub some colors here and there but White ub PFP (will show through for the text) + 5 top colors, preferably wow (or at least for the gradient colors). Print will be a little thick v. doing it in 7co but I wouldn't hesitate to run it that way, just choose your white mesh carefully.
Don't be afraid to make art suggestions to your client that involve color reduction, remember most people aren't thinking along those lines, they just have a logo and that's as far as they've considered it. They'll be stoked you saved them a print color or two and you'll still be able to run the job in house.