You don't need to hold humidity in the whole cage, just a couple micro-climates. Make a couple standard humid hides and place one on the warm side, one on the cool. If you are unaware, a standard humid hide would be a rubbermaid tote (lid still on) with a hole just large enough for the lizard cut in its side and a couple inches of dampened substrate, like moss, added in there. Ideally you should put enough substrate in the whole enclosure to allow the monitor to dig its own humid hide.
If you are going to feed turkey, you must follow the SDZ diet exactly. Eggs do not belong in SDZ diet, even with the shells. Beef liver does not belong in SDZ diet. Reptivite does not belong in SDZ diet. Savannahs aren't tegus, blackthroats, niles, etc... they are insectivores and to my knowledge, only SDZ, in its original formulation, has been successfully used to raise and breed successive generations of insectivorous monitors.
The recipe is 2.5 lbs lean ground turkey, 22.5 grams of bone meal, .5 crushed centrum tablet (regular, not mens, not womens, not silver, etc). You may need to order the bone meal from the internet, only 1 store in my area sells it and none of the major chains seem to.
To put it together you will need a pill cutter, mortar and pestle, gram scale, mixing bowl, and stout wooden mixing spoon. Ground turkey is typically sold in 1.25 lb increments, so it is easy to get the 2.5 lbs measured out (2 packages). Add the turkey to a mixing bowl. Cut the centrum pill in half, grind half into a powder. Place a small dish on your gram scale and tare it out. Add bone meal (make sure to get the supplement intended for human consumption) to the dish until the scale reads 22.5 g. Mix the vitamin powder in with the bone meal, then mix this in with the turkey with the wooden spoon.
From there place the mixture in ice cube trays and freeze it. I recommend trays that have their own lids to avoid freezer burn. Trial and error will dictate how much you need to thaw every day to feed the monitor while keeping it at a healthy weight.