Prior to profiling, it's essential that profiles be disabled on the workflow software and that a fresh linearization/calibration be performed. These processes do drift so having a fresh calibration prior to profiling is essential. The media settings that you are talking about are basically DMax aim points for the calibration process - those aims are different for each paper type.
I'd encourage you to profile with either Monaco Profiler or i1Profiler if possible. IMO, ProfileMakerPro and EyeOneMatch, in particular lead to disappointing results in comparison. Pay close attention to your Perceptual rending options as they are key with silver halide printing. Save your profile as a spec 2 ICC profile for this machine. Depending on their version of the host software and/or workflow software they're running you might be able to enable the profile within the workflow software so that everything is converted to the printer profile for this printer/paper combination. If their workflow software doesn't allow you to use the printer profile they'll need to *convert* (not assign) all images to the printer profile in Photoshop prior to printing. Again, this depends on what workflow software they're using (Labtricity, ROES, DP2, etc - you didn't mention this so it's hard to know what they might be using). Looking at the bigger picture of their workflow and integrating color management elegantly is very important.
Don't assign the printer profile to the monitor! The images themselves need to be *converted* to the printer profile either in Photoshop or the workflow software. In Adobe apps you can use the profile for soft proofing by going to View>ProofSetup>Custom. Pay attention to the rendering intent and other options and save your proofing settings as a ".psf" file.
Don't distribute the profile to their customers! That leads to all kinds of problems. The lab will want to update their profiles regularly. If customers have profiles then they'll start converting the images (which isn't their job) and when profiles get updated all their customers will have outdated profiles. Instead, distribute the Adobe Proof Setup FIle (.psf) so that their customers can soft proof. That's what customers need to do - nothing more.
Lab wide color management can be a lot more complicated that it seems at first. It's important to make it elegant and fool proof. And it's also important to keep it simple for the lab's customers. I've been working in digitally based silver halide labs for over 16 years on color management issues and have great relationships with Noritsu, ZBE, XRite, Express Digital, ROES and others. There are a lot of silver halide specific tips and tricks to implement along the way. Let me know if I can help.
p.s. Your friend should so choose the paper and chemistry they use carefully as there can be significant differences between them!