Take some time, save some money, do it in stages... and upgrade the speakers along with your new amp.
I do recall that when I had my speakers upgraded, the stereo shop didn't just pop the new speakers in. They said that that would not be a good, tight fit. They made these little speaker mounts to help get a secure mounting to the door. The bass response of your speakers will partly depend on how securely they are mounted to the door. Again, save some money and have it done right (if you are not a DIY guy).
Good luck and happy listening.