Is my ceiling too low?

Add some diffusion on your ceiling. Auralex makes some excellent diffusors. I have a similar basement ceiling problem. As Viridian noted above find the first reflection points and use a combo of diffusion and absorption panels. This can really make a differnece and overcome some if not most low ceiling problems. Look at my system for some ideas if you want. In most cases you wouldn't have to go to the extreme coverage like I did, but I have a dedicated room, and I please myself, this arrangement sounded best.

7'9 is still pretty tall, actually insanely tall for a basement. I think you'll be fine.

you're fine....don't hit your head

Your lower ceiling is only a problem in that you're getting more reflection in time vs. direct sound from your speakers, all things equal. If you sit closer to your speakers, this isn't an issue so much. Also, more "controlled focussed speaker designs", dipoles, Dappolito's, etc, tend to cancel out off axis (vetical) frequencies some what, minimizing ceiling/floor reflections...this helps. Otherwise, you need ceiling treatments more likely than higher ceiling. Again, if you sit closer to your speakers this negates these issues quite a bit, and helps.
On the other hand, if your ceiling height ratio,vs one of your length modes is within 5% of each other (7.8 and 15.3 in your case), you'll also have doubled up bass modes in certain ranges, which will definitely compound problems acousticall as well!! Proper speaker/seating becomes even that much more critical, and even some of this new EQ stuff on the market, like Rives PARC, or more DSP bassed stuff that's now arriving. Good luck

You are right, I didn't notice the length/height is so close to 2! This will be a bigger problem... Anyone can tell which case is worse: length/heigth=2 or length/width=2? or the same?