The other thing one can do is use ColorThink Pro's Color Worksheet and 3D grapher functions to visually see ever colour that fits within a profile space by overlaying the patch data with the gamut of the paper/printer profile. I believe this should be a lot more precise than using Photoshop's gamut warning.
I agree. Much better. However, I found that as long as you are 20 dE away from the gamut mask the colors are in the printable gamut. The advantage is there is no need to own any other software, just the measuring device.
However, that's what I did 10 years ago as a free, crude but effective quick check.
My preferred tools these days are Patchtool and, for detailed analysis, Matlab. For this purpose Patchtool has a built in patch generation for creating similar in-gamut Lab patches. It outputs both tif and CGATS with an excellent compare tool for checking the measured print results. It's also only about $100 or so. Patchtool is hard to beat for cost/value in print accuracy testing.
I've had Colorthink Pro for almost 10 years and it makes some beautiful plots/graphs but find it much too slow when working with a large image color set. Matlab runs a couple orders of magnitude faster and, being program oriented, makes it much easier to do custom "what-ifs." Most of the stuff I do/did was creating specialized test charts where Matlab can do what just isn't available with any other tools I've seen. But it's also very pricey w/o an academic subscription.