In 1980 I published an article in the Baltimore Jewish Times called, "What the Matchmaker Did and Didn't Do for Me." I interviewed many matchmakers and their clients and made myself (then single, of course) a guinea pig for a Boro Park matchmaker. The matchmakers make it pretty clear, that they take the time to find someone who is appropriate for you, and then, if there is an engagement, he/she gets paid on the engagement. Back then the fee was $1,000 to $5,000. I have no idea what it is now. My matchmaker also stipulated that I could only go on three dates -- if we don't feel the spark after three dates, then it's over -- move on to someone else -- "I'm not in the business of making you friends," she said. It was clear also that if I make an engagement that doesn't make it to the chuppah, too bad -- no refunds; she did her job, and may have even had expenses (some matchmakers work internationally, finding matches between couples in different countries). Since then I've become an attorney.
Let's assume that these same conditions were given to you, and lets assume that unlike my matchmaker, you actually had a written contract (this makes it easier for analysis in American and Jewish law). The matchmaker introduced you to your bride. His or her part of the contract was fulfilled. You went over your date limit, for sure, but you still made an engagement. In what way was the bargain not fulfilled on the part of the matchmaker? Even if there were no contract, going to a matchmaker and asking for a match is like going to a barber shop and sitting in the barber's chair. In the latter case there is an implied contract that you wouldn't be there if you didn't want a haircut, and you are expected to pay the going rate. Similarly, when you go to a shadchan, ask for his or her time and expertise to find you a spouse, your only way to avoid paying is to not get engaged to that girl. Very simple. The shadchan takes that risk, and the risk you take is that the shadchan will be successful and you'll owe him/her a few thousand dollars. It is not right or legal for you to benefit from the contract and not the shadchan.
So, in closing, mazel tov on your engagement. My blessing to you is that you should have a very good paranasah (earnings from a job or business), enough so that you can pay yeshiva tuition for many children, pay off the shadchan, and build a bayit nee'man.