[27litres]

Delivering 7psi boost on 11:1 compression with indirect injection is asking for trouble anyway.
My idea with an air tank is to use a relatively small one and drive an air drill/die grinder type arrangement with it to spin a turbine.
10-15 thousand rpm with high torque should get some decent boost.
You'd need high pressure in the tank though (100_150psi) which I'm not convinced a 12 volt compressor could deliver, which means a mechanically driven compressor, which results in mechanical losses at which point you may as well supercharge it...
(How's that for a circular argument!)

As for delivering extra air, that's only half the story.
Air in and of itself will not give you power.
What it gives you is the ability to burn more fuel.
Providing as little as 10% more air to an engine will go beyond the ability of the injectors (and ECU map) to provide sufficient fuel to burn at the ideal stoichiometric ratio of 14.7:1 (minimum air:fuel ratio at which complete combustion occurs and therefore provides maximum efficiency).

So without adding more fuel you're wasting your time.

You end up with a lean burn which beyond being a waste of all this air you've gone to the trouble of generating, actually burns hot, thereby reducing engine efficiency too.

Similarly with NOS. NOS in and of itself does not provide power. It provides a very rich and dense oxygen mixture with a lower stoichiometric ratio than that of regular air - the same volume of NOS can burn about 30% more fuel than that of air and achieve complete combustion. It's stable and won't explode like pure oxygen might.
But it still needs fuel.
Most NOS comes as a 'Wet Shot', which contains fuel at the correct ratio to burn. That's why they call it "power in a bottle".

One idea I have been playing with is some sort of water injection. They use it in turbocharging to create a cooler denser charge in the cylinder, but beyond that steam has a higher expansion ratio than air and won't affect air fuel ratios. So adding a small volume of water (we're talking droplets here!) might improve the energy of expanding gases during combustion as it flashes to steam and might slightly improve engine efficiency as it absorbs some of the heat energy.
Though like most things, if there was something in it someone would already be doing it!