Yes! I would install the backing so it opposes the belly grain. Living in a high humidity area will effect the m/c of the wood so you should keep it in a hot box or in the a/c at home when not in use. Add 3" of Perry reflex at glue up. You should floor tiller the belly so you have a nice even bend on both limbs before you add the backing.
Some of Dan Perry's(Perry reflex) flight bows are hickory backed hickory and he has won world flight competitions with these bows. Dan lives in Utah and the world championships are usually at high altitude in dry climates(like Utah) so his hickory bows do very well.
Hickory preforms very well at 6% moisture content where most other woods will break at that low of m/c. 9% to 11% is ideal for most other bow woods but hickory will be sluggish and take more set at those higher m/c rates.