Mortgage Questions

So, I'm trying to do this math and it's hurting my head.  Maybe someone here will have some experience or some expertise and help me figure this out.

7 years ago, I started a 30 year mortgage for a $205k home.  We paid practically nothing down, so the mortgage was essentially for the whole kit and kaboodle.

At 5.75% (I think) this left us with 3600 payments of $1400ish to make.

7 years later, due to overpaying each month, we have 20% of the principal paid off (a little over $40k), which represents about the 15 year mark (give or take) of the mortgage.  Meaning, had we been paying the default payments, it would have taken us 15 years to get here.  We are currently paying $2200 a month (the $1400 + $800 on principal) hoping to have the thing paid off relatively soon.  I made what I think was a mistaken assumption- if we were able to get half way (15 years) into the loan in 7 years, by paying the same or even more each month we would close out the remaining half in about the same time.  Seeing how we still have the majority of our principal left to pay, and a ton of interest as well... I guess the 2nd half of the loan doesn't compress at the same rate as the first half of the loan since the interest is all subject to change based on paying early- but the principal never will.

Alright-

We can get a 15 year loan for the remainign 160k at 4.5%.  Strangely enough, the monthly payments don't really change.  If you look at it like this: There are 23 years left in our 30 year loan (which isn't really true) and there would be 15 years left in a new 15 year loan- then it totally makes sense. 

But here's the question... If I continue to pay $2200 a month on my old 30 year loan at 5.75%, how soon will I really have it paid off?  Conversely... if I pay $2200 a month on a new 15 year loan at 4.5%, how soon will I have that paid off?  The people offering the 15 year loan say it will have $7k in closing/refi costs- which seems high to me, but I don't do this very frequently.  Does the lower interest rate get cancelled out by $7k closing costs?  I believe thats the same question as "which loan, with the same payment, is paid off sooner?"

Thanks.

If train A is leaving station B...

The mortgage company selling me the 15 year loan thinks that is my best option.  My current mortgage company thinks I should stay with them.

I have this one: http://www.mortgagecalculator.org/

But it doesn't tell you much about what happens when you pay more than your bill.