Is it possible that the wax rubbed, rather than melted, off onto your camera's LCD? Even though you can't scrape the wax off, it still may wear off for a while after you first start using it, especially in hot climates where it can soften up. What's the typical temperature outdoors there? Somewhere around 35 C? If this were something other than the F3, I'd say to just let the inserts "collect" the wax; since that doesn't use inserts, that's not really an option.
You didn't mention the brand camera you have. Canon's LCD is actually behind a very hard (acrylic or glass depending on the model) cover that you could safely clean with very small amounts of something like "GooGone" or other citrus-based cleaner/solvent. As to your lenses, lens caps should keep anything from getting onto the glass while they're in the bag; I'd be more concerned about the wax building up on the lens barrels (or camera body) as a sticky coat and then transferring to unwanted places via your hands.
You might check with your dealer and see if the wax impregnation on your bag seems similar to that on other models of the Waxwear bags, or if other customers have encountered similar issues (and how they've dealt with them).