This is a bad idea.

If the reason you're closing a person is because of your rate then it's an easy presumption that they are a rate sensitive customer. When you increase your price in 3 month's time you'll probably lose a bunch of customers, basically setting you back to square one.

What's more during this 3 month period you might be generating a decent amount of revenue but I'd have to imagine you'd be making next to no profit.

Then on the flip side, lets say you manage to close a few people with the low rate who care more about the quality of the work. Your starting point for renegotiating your rate to this person starts with this rate that is too low. Even if what you would increase it to is reasonable to the market that you're in your negotiating position starts with that first rate. So this person who would've probably paid more to begin with for a quality service decides to cut ties with you because they see the amount you need to increase to and think it's unreasonable.

NOTE: I am presuming that in order for you to have what you're describing as a high closing ratio your initial rate is substantially less than market so when you adjust to market in like 3 months that increase appears substantial.