Is it a bad/good idea to cut the bottom of the doors to mount speakers in...

[AZGrower]

I too would vote for the 6.5" component set, which will give you much better flexibility and response. Have you considered building some fiberglass baffle/pods that you can mount to your door?

Or you can go the route of kick panels, which can also work very well especially with the imaging like previously mentioned. These are pretty easy to make using fiberglass.