Writing a Master's thesis for 2 years ... is that appropriate?
Of course it's hard to say without knowing a lot about your specific situation, but I doubt spending an extra year on your master's thesis would be worthwhile.  In particular, if your advisor doesn't think another year is a good use of time, then I'd bet he is right.

Completing a master's degree is not necessary before applying to Ph.D. programs in mathematics in the U.S., and the primary purpose is to make up for a weak background or to shift fields.  From this perspective, the main goal is to do good work and move on, not to spend extra time trying to accomplish even more.  That comes across as eccentric, like you are wasting time on a side track rather than moving on with your academic career.

Two years in a master's program is the upper limit for what's normal in mathematics in the U.S., and this includes coursework.  Spending two full years working on a master's thesis would be unusual.  If you spend an unusually long time on your master's thesis, it may look like you just weren't able to write one more quickly, either because you weren't adequately prepared or you aren't good at getting things done.


  I thought that expanding the scope of my thesis, even if it would take longer for me to complete and defend, would look even better on my Ph.D applications.


If you write a much better thesis, it could be worthwhile, but it needs to be dramatically better even after normalizing for the time spent.  Linear scaling can't help you: if you spend twice as long writing a thesis that looks like it involves twice as much work, then it won't end up being a significantly better demonstration of your abilities.  The only real benefit is if your thesis is much better than twice as good.  (For example, if you have almost proved a significant new theorem, you might be better off taking longer and actually proving it.)