Hi there. I take it the Selmer C** is the S80? I've had a couple of them and found them like blowing into a sock. Rather than getting an even closer tip opening than the C** (which is already really narrow) you might want to try a more free blowing mouthpiece. Maybe a Yamaha. All the plastic Yamahas are also very closed tip openings, but a 6c might be OK. Otherwise, try an ebonite Yanagisawa 6. These are free blowing, very well made and have a good tone. You can often pick them up from eBay for a reasonable price as people buying new Yani saxes persuade themselves they need a mouthpiece other than the one supplied by Yanagisawa.
If they go into a shop and someone suggests an Otto Link, think carefully. Just my opinion, but I find the ebonite ones very, very stuffy.
Another option would be a Runyon Classic or Jody Jazz Classic - they're pretty much the same. Just watch out for the opening numbers - Runyons are quite different from others. A Runyon 7 sounds pretty wide opening for alto, but in fact it's a narrower opening than an Otto 5.
Jon
PS - Practising more also helps switching between alto and tenor!