You don't need to worry about density. Boeing needs it because turbine engines traditionally manage fuel quantity in terms of mass (lbm or kg), whereas we use volume (litres or USgal), which can be measured directly just using capacitance.
Also, 28-bit resolution may be much more than needed, depending on the capacitance range of your transducer. The Van's capacitance plate setup (one at each end of tank) gives a range of very roughly 150pF (empty) to 300pF (full of avgas). For my RV-8's 21 USgal tank, this gives about 7 pF/USgal. The precise numbers will vary a bit depending on details of tank construction, but they won't be too far from these. If you then use a 10-1000pF transducer, for example, 12-bit A-D conversion would resolve about 0.25pF, or better than a tenth of a USgal.
I've developed a similar system, using an Arduino with 10-bit A-D conversion, and get good results with it during initial bench tests.