I'm getting to this thread a bit late (been out of town) but glad to see some progress has been made. Josiah, good on you for taking on the advice being given, too. Basking spots and substrate have been covered and those are both very important changes which needed to be made. One of the things that Mr Boyd touched on which is also important is the size and location of vents and the number of hide spots. I apologise if someone else has covered this (I've skimmed over most of the thread, as there is seven pages worth!), but if it were me looking after that lace monitor I'd build a glass-fronted plywood enclosure rather than use an all-glass fish tank. There are a few reasons for this, but the most important are:
1. A custom built plywood enclosure can be front opening, meaning there are no openings on the top. An aquarium has to be top opening. At the moment you have a screen lid, which means that any heat coming from the bulb goes straight up through the top, taking valuable humidity with it, cooling and drying out the enclosure. In winter this is even more of an issue because there's a rapid drop in temperature between the basking spot and the rest of the enclosure. Lace monitors are highly unlikely to get burned if they bask on a hot basking spot as long as the air temperature is warm around the basking area. My adult lace monitors have basking spots that hit 60C mid-summer and have never suffered a burn. However, if the basking spot is hot but the monitor still feels cool because of the surrounding area being cool it may bask longer than is safe, getting burned. The dryness caused by the warm humid air rising through the screen lid is also a huge issue and was exacerbated by the sand substrate you had the monitor on to start with. I suspect that the oozing you are seeing coming from your monitor's skin is either shedding issues caused by the desert-like set-up (sand substrate, screen top) or burns.
2. Glass aquaria are very poorly insulated. Not only is the heat rising up through the screen lid as mentioned above, but the heat escapes through the glass as well. A thick plywood enclosure retains the heat. If you're trying to keep a reptile active and feeding right through winter in Australia you're going to be up against it with a glass tank. Even heat pads or heat cords aren't going to do, for the air will still cool off quickly away from those heat sources because the heat escapes so easily through the glass.
3. Having a custom enclosure with front rather than top access is better for keeping interactions with your monitor on a calm level. Monitors hate being approached from above for they'll usually see you as a predator and act defensively.
You may want to consider investing in a non-contact temperature gun, too. Much better than a digital thermometer for gauging temperatures for you can measure the basking surface temperature in under a second and that is the most important temperature you need to know. You don't need an expensive one and there are many inexpensive ones available these days. I think they're a must for any reptile keeper, but particularly for monitor keepers.