Thicker strings will give you a meatier tone for stuff like blues & jazz...fingerpicking etc...
But for tapping stick with the custom lites... you're using the same guage I've used for years and the upper guages are small enough for easy tapping and lead bends and the lower strings are thin enough for bends but thick enough to give some chunk to power chords.
Best bet is keep a second guitar around with thicker strings. That way you can leave your first guitar set up with lower action and light strings when you need em.