No point in salvaging any of the stock stereo. If you're going to do it, replace everything. Plenty of people have built enclosures into the quarter for a single 10" which is the standard. Mini sub's work pretty good too. I have a pair of elemental designs 6.5" in my Camaro that sound like a single ten but they are gone now. Parts express.com has Tang brand 6.5" sub's that have good reviews, I would try them if I wanted more mini sub's but I am working on a single ten for mine.
To avoid losing any storage or seating capacity, the rear quarter where that stock "sub" (a kind and generous name) is has been leveraged by numerous self-built enclosures (including new amps), retrofitted with smaller "all-in-one" powered subs (this is what I used - sounds like a "small" punchy sub with some music, perfectly fine with other - I don't love it but it made a noticeable and positive improvement and I ran the volume/frequency remote up to the front so I can control from there, worked out great), and some have simply replaced that aged turd with a direct replacement (usually also replacing the stock speakers and stock amp all around, good time to also swap your head unit). For examples of all these, grab a beer/coffee and start searching.....LOTS of examples out there of what Mudders have done.
That bracket you've got is nice to have - you might be able to slightly enlarge the hole to accommodate a slightly larger (8"?) sub and stick with the stock "open baffle" design there, coupled with a new amp as you mention. If you go that route, go with Pioneers in all the doors and replace the stock amp altogether for a HUGE improvement all around. If you're up for it, get into the dash and replace the head unit as well.
All told, I think I spent $300 on HU, door speakers, and powered Kenwood sub and it's a night/day difference over what was stock. Great investment, you'll be happy you did it. My personal recommendation on HU, I went with a "mechless" unit (no CD player) which has a USB port - I have ~1,500 songs on a mini thumb drive (literally the size of my thumbnail) so plenty of tunes there and because it's got no mechanical drive, NEVER skips while offroading.
For door speakers you can't beat component sets. They are slightly more work since you have to mount the highs and mids but worth it. Also go 6.5", its worth the extra work to make them fit. You can always get last seasons speakers on eBay for cheap, I got two sets of Kenwood 6.5 components for $60 each free shipping, plus a 4 channel clarion amp for 70.
I think you could fit an open airspace sub in there that doesnt require an enclosure. Although really anything you do will need modifying. And an open air sub probably wont be as full sounding or as hard hitting as a sub with a box. You could also make a small box to mount a shallow mount 10". Itd still take some space but much less than a standard sub. I heard a pretty good sounding shallow mount JL a few months ago, i dont remember the model it was though.
JL Audio Stealth Boxth comes in many variations and sizes I ended up going with the non Stealth ...12 inch angled sub box that sits next to my fridge. I built an enclosure that fit a 10 inch sub into the cargo area but it blew on a trip and would have had to remove cargo and the fridge so went with the angle box and it fit perfect and I was back on the road in 15 minutes.
I bet with a little modification one could find a Stealth Box that would fit and not take up much room
I built a removable box in my Drawer Build that has a 10" in it with a piece of expanded metal for the top to protect woofer.
Have not wired it yet, but excited to hear how it hits. When I go camping, I can put a sleeping bag or other junk in the hole.
I will post pics.
I thought that bracket you've got looked familiar - looks to be a "Hog Back" bracket intentionally fab'ed as an aftermarket piece for open air (open baffle) sub mounts. My $.02, take advantage of that thing and learn from those using that specific bracket which amp/sub combos work best and just get the new pieces accordingly....
....or go banzai and fiberglass in your own custom sealed enclosure and spend a month doing it in the process.
I didn't even have a sub, didn't realize it was the stock bracket, thx for that. Regardless, it's not sealed or boxed, hence the quoted reference (akin to an open baffle would have a better way to put it). I'd still suggest to the OP not going overboard or over-thinking something back there - that bracket fitted with a decent larger sub (and an improved amp) could likely be had for what I spent on my kenwood powered sub and probably sound noticeably better and preserve his cargo space.
As for my box taking up space, of course it does, can't change that. But I have the box tucked up against the back of the front seat (the back is angled the same way as the seat, and the second row seat is removed). It sits above a small box in the foot-well area, hinged at the front so I can tip it forward and store stuff underneath. Essentially serving as the lid on the box. So at least it's in a place that's not the best storage space.
I only use my "sub" as a woofer. No hip hop trunk rattling here. I've got components in the front doors and the 12" in the back crossed over at 160hz serves as a kick-ass woofer for the door speakers. It's like having two home speakers in the front of the truck! Each with a 1" dome tweeter, a 6-3/4" mid, and a 12" woofer.
Don't waste your time on an "open air" sub. That s like building a light duty rock crawler. Sub's are for deep base and you will get the most with proper enclosure. And its about full music not just bumpin.
OP - below is a pic of my install of the powered Kenwood sub I've got. Again, it generally sounds great and makes a huge improvement although is obviously at times (certain music) a "small" and somewhat punchy sub. All things considered, I love the installation and fact that it is tucked away without compromising any storage or seating (one of your objectives).
as long as you're not using a Wagon Gear tailgate, you might consider mounting a 10" sub in the tailgate:
I used 2 nails and a string to mark the 9.25" opening that is required (some speakers might need slight larger). I used a cutoff wheel on a dremel tool, then ground off the burs and vacuumed out the debris. I then painted the exposed metal so it didn't start to rust out...
using the mounting clips as reference points, cut out the same diameter hole in your tailgate liner (a rotozip or other rotary saw is really nice for this).
Measure and cut a piece of 1" MDF to fit the area to eliminate vibration in the tailgate and to give you more mounting depth. Wrap with carpeting or other material.
While everything is out of the way, go ahead and run your wire through the rubber tube used for the door lock control wire. Also, it's a good idea to put some sound dampening in the tailgate while you've got it open.
Lay everything in place (liner, MDF, speaker) and ensure it all lines up.
If you're good, then go ahead and drill your holes for the speaker mount, then remove the speaker. Depending on the screws provided, they may or may not need to go through the tailgate itself. Check your depth before you drill to prevent extra screw holes in the sheet metal (I HATE rust, so this was important to me....)
You'll need to secure the MDF to the liner and the tailgate. (I used 6* 1 5/8" deck screws) Pre-drill the holes, then screw em in. I split the difference between each of the speaker mounted holes.
Connect your speaker wire, install the speaker, enjoy your upgraded tunes!
Edit: Adding some pics showing measurements of cuts, etc.