Pictures get a little scarce here, but the next steps involve:
1. Mounting the new speaker onto the adapter.
2. Soldering speaker leads and clips onto the stock speaker wiring.
3. Test-fitting the speaker + adapter multiple times.
4. Trimming plastic off the adapter mounting holes to improve the front clearance.
5. Transferring the foam insulation off the old speaker to the new speaker to protect the front, reduce the possibility of rattles, and reduce movement (important because...)
6. Finding out that either the front two holes would line up, or only the rear hole would line up. Here again you get to choose which path to take.
Finished product, pre-installation:
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Overall, I'd give these adapters a B-. They are useful if you don't want to modify the stock speaker mounts, but I would have a drill, a hacksaw and maybe some plastic card handy for modifying the adapters as necessary. Also, following the instructions and taking the door panel off first might improve the fit.
The new coax's provide a noticeable improvement in mid and upper frequency clarity, along with some increase in midbass. I'm hoping they'll fill out as they break in, but with the currently less-than-secure mounting and lack of an amplifier, I know that there's only a limited amount of additional oomph I'll get out of them.
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* Update: After thinking about it some, I went back in and played around with the bracket some more. I was able to get it to attach to the door at three mounting points (instead of just one), which resulted in noticeably better sound from the speakers. Also added some plastic sheeting behind the speaker, to provide some water and dirt protection to the magnet.