"...Am I going to regret skipping the bass?..."
In a word, yes.
You don't need boxes full of 12 inch sub-woofers. But at the very least you do need a single 10" speaker somewhere.
I'm not saying this will work in a Miata, but in my car (a Taurus station wagon) I have had exceptionally good results running a single 10" Orion Cobalt series dual voice coil speaker and breaking all the rules: I am running it full range (not crossed over for 90Hz and down like it is supposed to be) and running it free air (not in a sealed enclosure like it is supposed to be) and I have finished in first place in sound quality in every IASCA competition I have entered this year.
The Miata sounds like a tough way to go, though - you're like a pickup truck in that you have very limited amount of cubic feet of air volume for the speakers to work with. It's hard to get good sound in those circumstances. ;-(
I've never experienced speakers in headrests before, but I can't imagine that it would be very easy to balance them with the other speakers in the car... I could be wrong, though, no first hand experience there.
If you can find a way to mount a single 10" speaker in your trunk (try it sans box) so that it plays right into one of the seatbacks or maybe between the seats (is there a pass-through for long items in the Miata?) I think you would be well pleased with the results.
And if you could find a way to mount a pair of MB Quart RKB-100 4" co-axial speakers in your dash right at the corners of the windshield, you would be absolutely blown away. I agree with you about being skeptical of putting tweeters down by your ankles!
Good luck, let us know how it turns out.
tanstaafl.
"There Ain't No Such Thing As A Free Lunch"
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"There Ain't No Such Thing As A Free Lunch"