Filter and signal processing requirements are conflicting for all 3 functions necessary for DC tilt , gyroscope rate motion and tap impulse detection. A touchscreen is often preferred for tap sensing which are very short levels of contact pressure, wheras tilt or relative XYZ position is the 2nd integral of acceleration down to DC.
Can you define the processing power available?
i suspect tilt and shake sensors are slow (<10Hz) and may not have the bandwidth to detect a tap impulse in the >1KHz range, shorter than tilt BW, but I'm not sure unless it has peak and hold detection to compare with average sensor capacitance.
These are tradeoffs for parallel signal processing, which might be simple in end solution such as analog detection of impulse taps and digital lookup tables for tilt and rate motion.