My initial thought was there's no way the writers will be happy with your attemp at a
network sitcom look, so don't even attempt to do that. So don't. You don't have the experience or equipment needed. Are you shooting in a
theatre with pipes/catwalks? Will there be multiple cameras? If so, how many? Will the cameras have large sensors that can reduce the depth of field and
throw backgrounds out of focus? That's especially important for achieving that "look." I have way too many questions.
With your experience and equipment, forget going for harder shadows on the talent like one would see on "Friends" as opposed to say a 70's sitcom such as "All in the Family." You'll need to go with a softer look or I believe you'll have a rough time attempting this. You can minimize the
flat look by using soft light from the front, hard lights on the backgrounds and increasing the backlight. On closeups, you'll have some modelling, reducing the
flat look. This is a sitcom. You're lighting for closeups.
Network sitcoms are shot with precise camera angles, lighting angles and exposure levels. I doubt that you will be able to do that.
So instead, you'll need to make your hard sources softer using diffusion or by bouncing. Your set-up time will be quicker because the flatter lighting is more forgiving of last minute changes to
blocking, where a
key light suddenly becomes a ¾ backlight.
As stated before, forget using the cheap
LED's on faces. Maybe use them for the background where they will do much less damage to your images.
For soft frontal fill, I'd shoot the
cyc lights with their
broad spread, through large diffusion frames. You can make lightweight frames from strips of wood, metal or even cardboard. Hang them with coat hangers or whatever. The bigger the frame, the softer the light. Position the light so it fills the frame completely. You can then control hard
spill light using homemade flags or cutters. There's all kinds of DIY info on the internet including using those $20 , 500
watt tungsten work lights from Home Depot. They can come in handy when softened with diffusion. With 500
watt globes, they are HOT. Globes range in wattage from 100 to 500 watts. Use the minimum wattage you can get away with. Hang the the lights
downstage at a fairly low vertical angle to minimize facial shadows. To prevent light levels from building up in the center of the set, space them out evenly and don't focus them so that they're crossing each other.
Your fresnels can be the key lights. Depending on how many actors there are, or if there is a lot of movement, you can light actors individually or key areas where multiple actors are covered. If keying for broader coverage, use two, three or four fresnels positioned
downstage. The vertical angle can be a little steeper. Use fresnels at full or close to full flood which gives a softer beam, makes for easier blending with each other and lets the barndoors make harder cuts.
This method is more from the 70's where sitcom lighting was flatter and not at all like the lighting on Friends or Seinfeld. The advantage is that it's more forgiving regarding camera placement and movement and once in place, requires little or no adjusting between scenes. Your
fill light levels might range from a little less than the key lights to even twice that of the keys. That old "rule" of key to fill ratio was meant to be broken and it's broken all the time. Just look at the lighting on about any news set.
I say all of this because with your lack of experience and what you have to work with, getting the look that the writers want would be a monumental task, perhaps for even the most talented television lighting designers. Good luck!