It does look good.. the prep work looks great.
You scare me though... saying the doors don't have drains!
ALL (repeat after me... "ALL") doors have drains!
Do NOT seal the bottom of the doors, there ARE drains.
You block them off, I give your doors one year, maybe two, before rusting out from the standing water.
Also...
Remember, your speaker needs a baffle or an enclosure to work properly.
The size of the enclosure or baffle determines how low it can play.
If you build an enclosure, then the enclosure also determines how much power you need to make it play loud... the smaller, the more you need.
Or, in other words... an enclosure could make your speakers need more power than they otherwise might.

So, I'd recommend the simple "baffle" route.
...but, look at your inner door skins. Big holes, covered by a thin plastic sheet. Think that plastic sheet makes a good baffle?
Not even close.
You are installing the speakers on the inner door skin metal surface... so THAT is the surface that must prevent the sound coming off the back of the speaker cone from leaking around and cancelling the sound coming off the front of the cone.
And, the thin plastic covering the big holes isn't going to cut it.
The cancellations get worse, the lower in frequency you get...
So, the most noticable issue right off the bat you'll hear is a lack of midbass, the way it is now.