I don't know the play, but have lit a few similar type ones!
Divide across stage into two main areas, leaving an avenue between. Leaving about 4? upstage  as the Disney World across the CYC.
Set the Medical & the house areas, with all the furniture positioned almost off stage on each side. Keep the furniture to a minimal, such as a desk on the incline & sofa or whatever on the opposite incline. Leaving as much acting area in the avenue as possible. If your stage is raised, depending how high, you can use the Apron or the auditorium floor, to bring the acting area down.
This will give you the 3 areas that can be easily lit separately.
Assuming the two light trees, will be on the far left & right of the audience.
Looking at the stage, I would assign the parcan lamps on the trees, from left to right as OP 1, 2, 3. & PS 4, 5, 6.
{Rotate the parcan hot spot which is elongated in the centre of the bubble [globe] accessed from the aperture at the rear of the lamp, buy gently turning the white ceramic electrical connection to the bubble to either a horizontal or vertical position [do this with no colour gel fitted, as it is easier to see the hot spot with open white]
                ?C?

    ?B?                                ?A?       ;           ;   
       ?Ave?                        

                Stage
1   2    3                                4  5  6
OP Tree                                    PS Tree

 
Focus OP 2 on to the PS  [SL] area which I?ll nominate as ?A?, [rotate the ceramic until the hot spot runs from US to DS.]
Do the same with PS5 on ?B? SR area.
OP1 rotate the hot spot to a horizontal position, running from PS [SR] to the Left of the centre Avenue [CS]. Do the same with PS6 on the opposite side. This will define the areas & give fill as well. {you can use Blackout foil [Aluminium] on or in your gel frame to give a fairly defined masking line, cutting out spill into the other area, as you would using shutters.}
Focus OP3 & PS4  in a horizontal bubble, on area ?C? pointed along running from SL to SR. You can use the blackout masking along the bottom of the lens gel frame, if you need to define the area.
If you use dimmers you can also cheat in either OP# or PS4 to give extra fill coverage &/or as a fade in support when ?A? or ?B? is being used. A good idea with OP3 & PS4 is to cross light the Lamps, so OP3 would light ?C? [SL] & PS4 ?C? [SR].
Also you could make up a set of ?Floats? [footlights] what I believe you may call ?Strips?.
The cheapest is to use individual Dichroic spots, that are normally used in Track lighting for shop display purposes.
You can get them from Commercial salvage yards or even Lighting Wholesalers shop soiled or damaged stocks, which have been returned from Lighting Stores & the Wholesaler has claimed a warranty credit from the Manufacturer on. It might take a few Comps &/or sweet talk, but I?m sure they will have a few pallet loads of damaged stock laying around.
?Birdies? {One under Par bubbles] Or the outdoor domestic flood lights, the cheap domestic BBQ spot/floods, are also good to use.
[There are colour gel frames available that clip on, rather than buying different coloured bubbles.] 
Mount them on flat wooden painted black boards [Turtles] as either Floats/Ground Rows or ?Z? [floor] lighting.
Also the small cheap outdoor ?QI Linear? bubble floods can be used to great effect - however they put out a lot of concentrated heat & tend to make the Gel brittle & leach the colour out, over a short period of time!
I hope this all makes sense? 


 

One other thing to think about would be making your own lighting gear.
If your Lampy?s {Techy?s] are enthusiastic enough, they could have a go themselves?
Of course if they are students avail yourselves of a friendly Sparky [Electrician] to test &/or supervise. As I realise in most of the US it is not a requirement to have electrical work in theatre, to be done by Licensed/Qualified Electricians, as it is here.
Even though your normal electrical supply pressure is only 120VAC, where ours is 250VAC, You have larger Current [Amps] to deal with, in the using the same Wattage. [It is not the Voltage that kills, but the current that does!]
Rather than getting into Ohms Law, a simple way to calculate the current of the a 1000 Watt Lamp is to;-
Divide the Wattage by the Voltage to give the Amperage.
1000W          ; Wattage
  120V         &n bsp; Voltage  = Amperage
= 8.3 A
or Volts X Amps = Watts
Where as here;-
1000W
250 V
= 4A

Also I believe the US it is a practice to use a lot of what you call Edison fittings [2 wire - Active & Neutral] without a 3rd wire Earth circuit.
In theatre it is a good practice & policy to use an Earth on stage appliances & it to be deemed an ?Earthen Situation?.
So may I suggest if you do have a go at making up your own lantern equipment, an Earth wire is fitted & bond it [Screw or bolt] to the metallic encasement body via the power supply plug top Earth wire connector.

Large Coffee Cans are excellent lamp housings. I used the large Baby Milk Powder Cans, when I was a young kid, because we only drank Tea & that came in a packet or Tea Chest!
The bay food milk cans where great because the inside of the can was reflective.
I used a can opener to cut out the bottom of the can & covered the bottom with Colour Gel. Using the lid of the Can to mount a globe electrical fitting [ domestic Bayonet Cap light globe holder - yours would probably be an Edison Screw type fitting] So when the incandescent globe mounted on the inside of the lid, could be popped into the Can cylinder with the coloured gel.
This was very primitive light, but I many years latter I made up a Cyc batten using the OLIO Olive Oil square drum cans. Fitted and held with a frame of Dexion shelving angle shape legs/uprights. Which was very effective & each Can had a 150 watt globe, there were 2 units of 8 lights each = 10amps in total.
But I?m sure with the cheap price of the outdoor & home handy workshop light fittings these days, they would be easier to procure.
At least you won?t have to get in too using ?Salt water Dimmers? these days - But that?s another story!