300 watts will move a 12 just fine as long as you pick one that doesn't need a mountain of power. A lot of subs these days are happy in the 300 to 500 range, so you've got options without touching the amp. The sub itself isn't usally what's holding you back anyway. The box is honestly the bigger deal. Going sealed to a properly built ported box is the biggest single jump most people ever make. Same sub, same amp, and it can sound like you doubled your gear. Ported boxes tune the air inside them so the cone gets help down low, which is exactly what you're describing when certain songs feel flat. That's where sealed boxes tend to fall off. I did almost the same swap in my wagon a while back. Had a 10 in a small sealed box and it sounded okay but never had that low rumble. Built a bigger ported box around 1.75 cubes tuned in the low 30s and the difference was night and day. Way deeper, and it hit harder even though nothing else changed. Downside is it took up real space and ported boxes get big fast, which matters when you haul stuff. Since space is tight for you, here's what I'd look at. Some subs are designed to work well in smaller ported enclosures, so check the manufacturer's recommended box specs before you buy anything. If a 12 wants half a cubic foot more than you've got, a 10 in a proper ported box might actually outperform a cramped 12. Box volume matters more than cone size once you're past a certain point.
Don't sleep on the existing box either. A year-old sealed box might just be leaky or undersized in the first place. Pull the sub out, check the seals, and look up what volume the sub actually wants. Sometimes the fix is free.
If it were me, I'd keep the amp, pick either a 10 or 12 with modest power requirements, and spend the effort building a ported box sized to fit your hatch. That's where your flat low end is coming from, not from being one cone size short.