In general a mouthpiece with a larger tip can allow you to get away with a softer read and mpc with a closer tip allows a harder reed, it's kind of like a clutch. Still, there is much more to it than that like chamber size the curve of the rails etc. A mouthpiece search can open up a whole can of worms.


If you like the Meyer you might try an Otto Link Tone Edge as well. Trying mouthpieces can be maddening, there are so many out there, some people go bonkers over it. I have found I have to use a mpc for a week or two before I decide on it, but then I have stuck with the same mpc for years now and avoided all that madness.


I was lucky with my tenor mpc, it came with an old Yamaha tenor I bought years ago, it turned out it was an Early Babbit hard rubber Otto Link and was worth more than the horn. Somebody had worked on it and hadn't done a wonderful job but I had it reworked by someone that knew their stuff and he restored it to what it was meant to be. I tried a bunch of mpcs over the years but always came back to the Early Babbit.  


I like the fact that you stuck with your generic mpc for so long, it shows you aren't an equipment freak, good for you. I have come to like a middle of the road mpc over a mpc with a huge tip distance. Some say a larger tip gives more power, though I don't know how you can quantify that. I like the flexability of a middle of the road mpc.


Also you should be checking for how a mpc affects your articulation as in ease of. You will probably have a harder time with a stiff reed and an open tip mpc. It just depends on what you are after.  You know, this is the kind of stuff you should be asking your teacher, that's what you are paying for.       
 

A Meyer tenor in size 7 has a tip opening of .086" - that's pretty small in tenor pieces.  The most commonly played size, over the last 40 years or so, has been the equivalent of an Otto Link 7* - that's .105".

While Meyer mouthpieces have long been a standard for alto players, Otto Link mouthpieces, in either hard rubber or brass, have been the standard for tenor players since the Blue Note days.  If you look 'round most any manufacturer's websites, they will often claim that their mouthpiece is either based on, or "better" than an Otto Link.  There's a good reason that it's so popular - the design works.

See if you can find some Otto Link or Link-inspired pieces to try.  One common one is the Vandoren V16 series.  They tend to have good quality rubber and good facings.  Check out the T6, T7, or T8 facings for something that may be compatible with your choice of reed.

If you like a lil' more buzz in your sound, consider trying a softer reed.  I wouldn't let a previous reed choice dictate my next mouthpiece.

G'luck!