I have done five models for you.
I have modeled this
new slime line 10" driver from Dayton Audio, in vented push pull alignment, in isobarik push pull vented alignment and in push pull sealed configuration. Note that for the isobarik enclosure you will need a total of 8 drivers for two subs.
I modeled this
10" Ultimax driver from Dayton Audio. I modeled it in sealed push pull configuration.
Lastly I modeled this
10" SDX 10 from Creative Sound solutions, in sealed push pull configuration.
This exercise confirms the power penalty of reduced enclosure size.
Now you have to look at these specs in relation to the final impedance. The isobarik and the SDX 10 are both 2 ohm. The others are four ohm. So for these designs you will need a 2 ohm capable amplifier.
The most effective sub is the LS10-44 vented. However it exceeds you volume criterion by 0.6 to 0.7 cubic feet when you take driver, port volume into into consideration.
The isobarik model has a performance almost identical to the standard version except the penalty of reduced enclosure size is a requirement for double the amp power for the same spl. It meets your size criterion, and I think would have a total internal volume of 2.2 cu.ft. You will have to be creative with the port however. I do isobariks mounting the drivers back to back and make the tunnel connecting them with circular wood or MDF spacers. Each driver in the tunnel is then wired out of phase with its partner so the cones move in the same direction. The the two pairs are obviously wired in phase so they push pull.
The sealed version of this driver does not have enough output and there is not enough driver excursion for Eq. I would not build that one.
The Ultimax and the the SDX 10 model virtually identically, except that the SDX 10 is 2 ohm. The enclosure size, spl and F3 are so close it makes not difference. The increased sensitivity is illusory as the amp power for the same spl will be the same because of the halving of the impedance.
Now the two viable sealed contenders and the two vented designs are all 12 db down at 20 HZ. At 30 HZ the sealed alignments are 7 db down compared the vented subs. However both sealed alignments will tolerate 6 db of boost at 30 HZ and may be a little more.
So you will need three times the amp power for the sealed alignments compared to the conventional vented, and twice the power compared to the isobarik vented.
Now when you build it, I would use threaded bars right though all drivers one side of the enclosure to the other. So either the two or four drives are strongly connected with the mounting rods. This is an old trick of Laurie Fincham when doing push pull.
If you build one of the vented try and see if you can make the port act as one of the braces. Fitting the port in the isobaric enclosure will take some ingenuity, but I believe it is possible.
Getting your mind round these models will likely keep you busy for a while. All except that one vented alignment with the slimline driver, I believe to be viable designs and meet your criteria for performance though one is a little large, although only the vented alignments will meet your criteria without Eq.
Both pay the same penalty of reduced enclosure size. The Ultimax has the slightly lower Q which I think might be enough to give it a slightly tighter but this may not be a significant difference.