Mouthpiece / Clarinet maintenance for Altissimo Register

I've played the clarinet for five and half years and am now playing music that frequently crosses into the altissimo register. I can play these notes, but they don't sound well and I squeak a lot. In addition to practice, are there specific mouthpieces or ligatures that would help improve the sound? I play #4 strength Mitchell Lurie Rico reeds and am still playing on the stock mouthpiece that came with my clarinet. Also, I've been having intonation problems for awhile now, and I was wondering if a new mouthpiece could help with that too. Thanx