I thought about advice on mouthpiece and reed.
But, other than the plastic-cover, he had generally good quality mpcs and reeds.
The yamaha and hite are generally quality manufactured mouthpieces. Doesn't the Hite allow for a softer reed from it's design (been a long time since I've tried one).
I wouldn't want to lead him on a wild goose chase of swapping mpcs and reeds at his experience level.
Something much better performed by a private teacher.
Once you start swapping mpcs you need to learn more about how the mpc was designed in the Tip Opening and Facings and baffle. Generally the shorter facing, larger tip you use a softer reed. ==>
http://www.clarinetperfection.com/clmpcTypes.htm
and how the reed which are all cut differently in length and depth, and even the part of the cane that was used can make a reed vary a bit, in addition to the type/quality of veins can affect everything.
Additionally, the player may or may not notice, which may or may not affect the way they play, of the final finish put on the reed.
I've found the LaVoz reeds now are coarsely finished, which prevents lip movement without picking up what feels like splinters on the lips. Versus Mitchell Laurie clarinet (or Hemke sax) reeds which are thin/long student cut but very nicely finished. When my son played alto sax I initially bought some LaVoz reeds locally. Splinter city ... I bought him Hemke's after I tried some then inspected each reed.
I had my daughter start out clarinet on a 1.5ish reed (hand finished from Vandoren 3.5s).
This for ease of play so she can work on the technical aspects of the clarinet.
She's now up to Vandoren 2s
I use from 2.5s to 4s depending up the mouthpiece.
If I'm lazy on my airstream/embouchure that reduces my reed strength by 1/2 to 1.
Student reed cuts tend to get water logged quickly, which affects consistent longer term playability, at least for me on sax and clarinet. If I play a long solo piece they'll get waterlogged and don't work on high notes without compensating. If I play much with a lot of rests/breaks then they tend to dry out a bit and continue to play well. They do tend to affect upper note a bit flat though if I don't compensate versus harder reeds. Tone tends to be a bit thin comparatively too. But nothing a student should worry about.
Back to the original question.
Reaching a Clarion C should be an airstream issue especially if a B is easy (assuming all else is well) as it's just shortening of the pipe. Thus more work on long tones.
Once you get to alternate fingerings and the Altissimmo register, where airstream is more important too, all the work down below will benefit. And if those are not attainable then a mpc/reed change may be in order assuming throat/airstream/technique are all well.
As you build up your airstream/embouchure it should be improved enough to move up 1/2 strength.
If you practice long tones on a 3 reed for say 1/2 hour. Then move back down to a 2.5 you should notice a significant difference in the ease of using 2.5 all up and down the clarinet. You may find that you don't need to use a 3 after a few cycles. Think of it as embouchure/airstream training.
Many newer players are not taught proper air support which will directly affect how high they can go with no issues. Using a harder reed brings that all to the forefront and can be used as a teaching tool. Of course, if the player gets used to it then they can move up on hardness too.
I still recall learning how to play a 4 reed on an 8 tip mpc on tenor saxophone, duplicating what Grover Washington used. Made my eyeballs pop up, and as I got older I got headaches from it. But boy ... was the tone full and woody. Anyways, it made my ability of playing softer reeds so much easier for any setup and any horn (except oboe).
I have a box of Vandoren 5 clarinet reeds somewhere too; good for injuries such as using for splints
