Have you considered infrared?
The lighting is cheap and easy. You can buy continuous IR floodlight strength lights on amazon (intended for home security, etc) for like $20, and they usually are LEDs, so they draw very little power and can run almost forever on a portable inverter in the middle of nowhere.
You can also use any of your existing speedlight flashes, which already produce plenty of IR light. All you need it a IR-pass filter over the flash, which they sell, and it will be essentially invisible to critters when it goes off, so you won't even startle them and can continue shooting more flash photos without them even running away.
In either case, add whatever normal diffusers you would use for visible, umbrellas and the like. You might want to experiment with umbrella materials to not make your lights intimidating to the critters. Lots of fabric materials are black in visible and will be inconspicuous at night, but white in infrared, acting more like a normal umbrella. If you use a digital IR camera (see below) it could be as simple as taking it with you to your drug store umbrella aisle and just pointing it at them to see which ones work.
The camera is a little less cheap, but not outrageous. For digital, you can get a converted point and shoot or old style DSLR like a Canon 20D or something for around $300 already converted to infrared (filters replaced at the sensor level to let in all available light and not require lens filters). For cheaper you could go with film, picking up any random SLR at a flea market for like $10, and then an IR lens filter for maybe $100, and some IR film rolls for a few more dollars. Note that if using film, you need to have a lens that has the IR red line re-adjustment markings on it for proper focus. For digital, you can use the LCD screen, but you might want a hood to block the light from it so as not to scare animals, or one of those LCD loupes.