Forget the green screen. I think a new fabric will be fine with the lights I already have. I just want the LED spotlight that I described.
I'm afraid I don't have much to go on to give a recommendation. It's actually tougher to give a good suggestion without more guidance.
In general, if you're doing video these questions are the minimum, and you might pass on two or three:
Beam profile: [shape and distribution] [Beam angle], like "Circle 5 degrees with sharp cutoff."
Light output: [Lux at distance] or [Total output], like "4000 lux at ten meters" or "500 lumens"
CRI: [Range], probably 90 with fluorescent, 85 with LED
CCT: [Range], probably 4000-6000K CCT. This one is most apparent and mixed CCT is damned difficult to correct in post.
Light source: [Real limits]. "Portable unit near cameraman's head, cannot be too hot. Must last stated time." LED and some incandescent or HID would work in that case.
Power supply: [What is available], like "Batteries only," or "xx Volt DC supply"
Runtime: [Time to run, time between recharges], like "Sufficient for 5-hour shoots" or "Eight hour shooting weekend without recharge" or "Must be wall power" or "Any"
Budget: [range], like "$300-$500"
From what I can tell, you've specified these things and skipped some biggies.
Beam profile: [shape and distribution] [5-6 degrees] (A mini mag lite has that beam angle, with spill though.)
Light output: Not a thing
CRI: ??
CCT: ?? (This one's very hard to fix in post)
Light source: "1 or 3 LED." But why not four? Or two? I can't tell if this is a requirement or a buzzword you've seen.
Power supply: 110v (wall wart, I assume) or 5v DC (USB power is usually limited to 5W)
Runtime: "Like usual" ???
Budget: ??
So far you haven't specified anything beyond what's available in the crap video lights section on B&H Photo sales. If you really can't think of anything else, the Stanley 10W LED with a beefier 12v power supply (1 amp, 12V) should run indefinitely in reasonable temperatures. It has high output, a concentrated beam, and is light. Budget: $50 for the light, $20 for the power supply, and duct tape to stick it on a camera.
More detail is better!