Reserved instances are based on a type and region, not on a AMI. Amazon automatically gives you the lowest price available to you when you launch an instance. So, if you have an m1.small reserved instance in US-East-1, the first m1.small instance that you launch in that availability zone, regardless of the AMI used, will be billed at the reserved instance rate, while every additional instance launched will be billed at the regular rate.
If you stop/terminate your first instance (and have other eligible instances running), another instance will be billed at the reserved rate (or if no other instances are running, you will not be billed). Likewise, if you stop/terminate an instance, and then start up another instance (such that you only have 1 instance running at a time), each instance will be billed at the reserved rate while it is running (stopped instances are not billed, and you get the optimal price for any running instance).
Do note that reserved instances are tied to both an instance type (e.g. m1.small) and an availability zone. If you launch your instance into a different availability zone, you will be billed at the full price (not the reserved price).
(Just to recap - changing the AMI has no bearing on the price you are charged for reserved instances as the reservation is not tied to the AMI/instance-id in any way.)
See the AWS page on Reserved Instances for more information.
As an aside, there are some cases when significantly overbidding on spot instances can work out to be cheaper than purchasing reserved instances. For the most part the spot-price fluctuates around the reserved instance price, however, it does, at time, exceed the the on-demand price. Depending on the particular instance type, region, and tolerance to cost variation that you have, using spot instances can be an option (you would typically have to bid 15x the spot price to ensure that your instance is not terminated by price spikes). Personally, I used this approach for some time fairly successfully, but recently decided to switch to reserved instances as the more constant costs made it more appealing).