Can adjusting handlebar height help reduce hand numbness?
You aren't the first to have problems with numbness riding, so take heart. You raised the saddle a lot, and that will transfer weight to the front of the bike via your hands. You have several options:

Pre-Ride:
* Buy some cycling gloves
* Raise the handlebars until they are comfortable (maybe an inch or so a ride)

During the Ride:
*Move your hands around the bar every so often. Road bikes have a lot of places to grip, and this is one of the reasons

If these don't work, then you could go to a bike shop and inquire about a simple fit. You could also do the same and look up how online. 

*My guess is that the reach from the seat to the handlebars is to short and to steep, which is great for a mountain bike that needs to be yanked around. It isn't the best for the stability and endurance needed in a road bike.