I have my antenna grounded but I don't see how it would survive a direct hit.
It won't. Part of the reason that mountaintop systems survive so well is several fold.
First, the fact that a high, grounded "unit" of the tower, feedlines, antennas, and in some cases a big metal "brush" on top actually helps to bleed off would be strikes so they cannot form.
But if a big tower DOES get struck, "everything is bonded to everything." Feedlines are bonded to the tower every so often up and down the tower. Just about ALL commercial antennas are a "grounded" design, that is, you'll never see an "open" (DC open) quarter wave whip on a decent commercial site. Of course Polyphasor or other surge arrestors are used at the bottom.
Extensive grounding "halos" are installed. Normally a ground ring of many ground rods is installed around the tower---I'm not talking about ground radials on a AM broadcast tower, but rather something like a moutain top VHF/ UHF site. Grounds are intentionally "rounded" around corners rather than nice neat 90* bends. All internal buiding racks, cabinets, AC/ ventilation gear, door and window frames, etc, is all bonded to an internal building circular halo, which is bonded to the tower ground.
All this helps to make a unitized, "spread" ground shall we say "object" that tends to act like a large gauge wire, helping to "unconcentrate" the hit, so to speak.
Your fiberglass monopole IS subject to explosion with a hit, as are commercial glass monopoles. Why some of them survive as well as they do is actually beyond me.
THE BIG THING with grounding is to try to help the strike/ bleed off go to ground BEFORE much of it gets "into the house."
This is why stuff like coax-fed dipoles and other ungrounded (not DC ground) antennas can be so very dangerous. A Polyphasor is not much protection on one of these.
Somewhere Motorola used to put out a booklet on site grounding practices. If you look around, I'm sure you can find it for download, or contact your local two-way shop.