The issue sounds more of limited oven temperature than how wet the cheese is. Pizza cooking tempatures optimally start at 450 degrees C upwards ie they can cook a pizza in around 90 seconds or so - but anything above 300 to 350 normally is fine and so lower temperatures found in domestic ovens often result in sogginess. My indoor pizza oven is set to around 400 degrees and is about right for me.

If you don't have access to a pizza oven - even home table top pizza ovens can be relatively inexpensive and some reach very high temperatures - then a work around would be to put an upturned frying pan or the underside (flat side) of a cast iron steak griddle in an oven that has a top grill and let it heat for twenty to thirty minutes or so under full grill heat - then turn the grill off, and oven on exactly as you carefully place the pizza onto the upturned frying / griddle pan. This will ensure that the base crisps as well as the top is cooking. So the heat may dry your top.

If the temperature is still a challenge then a starting experiment point for the cheese would be to make the pieces smaller so that more surface is exposed to the heat even down to grating if all else fails. On most people's home made pizzas it's the tomato sauce and raw mushroom and raw onion that gives the most moisture problem.

Hope this helps.