Appears I never responded to this - here's hoping the OP is still around 9+ months later.
Not mentioned was the potential for florescent, but that's likely going to be a bulky option with limited ability to control the light.
99% of the time I would not be able to connect any equipment being used in real time to a vehicle battery.
I might be able to return to a vehicle to recharge something for a while, off that battery, but that's as far as I will ever get.
As Ken_McE else has also inquired -
can you lug around a car battery? This is important because if you can, then there are many options for you depending on how much you can feasibly carry. If not, then your options are more limited since incan and arc lamps (HID, metal halide) require a lot of watts that smaller devices will have difficulty delivering for any length of time; a battery also allows for more flexibility since most small-ish, portable, self-powered devices that put out a lot of light will for your purpose effectively be tightly-focused spotlights.
Note that the term "car battery" is generic; a large gel-cell or deep-cycle battery might better suit your purposes if it's going to be regularly depleted to near-0% charge.
I only understood about 70% of your answer, but I agree that LED light is kinda overrated.
LED buys you options when it comes to runtime and/or light output for a given volume/weight that the other options do not. It's roughly double the efficiency of arc lamps and perhaps 4 times as efficient as halogen. It also scales in output far more gracefully since it can generate light from near-zero input power to its rated limit, while the other options simply do not dim anywhere near as well. Lastly, if you simply can't lug a car battery, it can still offer you thousands of room-filling lumens of light from small independent sources for a few tens of minutes.
I have no clue what you meant by 'variable output', (as it may or may not apply to my non-LED situation) but I'll look into it.
Say you have a 50W fixture, but that's either too much light for your situation or you need it to run for longer than it would drawing 50W and can live with the reduced output. With variable output you could run it for ~2x as long supplying 25W or ~5 times as long supplying 10W. LED is very capable of doing this with still relatively simple driving electronics; the other options not so much so without compromises in terms of performance or cost.
Summary is that I need to have ENOUGH light to make a decent photograph, but I also want to get to PLAY with these multiple light sources when I shoot!
I'm not sure your
couple of hundred bucks budget will grant you a great deal of leeway. Almost anything you buy ready-built putting out the kind of lumens you need to light large spaces will tend to be either ferociously expensive (ala anything "photographic") or require mains power and hell of a lot of watts (ala anything "jobsite"). LED lends itself to homebrew fixtures since it's DC-powered, generally low voltage, does not have the special handling requirements of HID, nor does it radiate so much heat as the other options. You might be able to hack some of the super-cheap architectural LED fixtures out there to take DC input so long as ">80 CRI", "super tight optical control", and "meets something close to its rated lifespan" aren't must-haves.