Ah1 my mobs is doing the ?Dairy of Frank Annie? on the 30th.
As for the Prac Pendant, just wire up a ceiling rose to support the light cable & feed the active switch wire from a ceiling Pull Switch, mounted on a suitable board or piece of wood. Mount it all to fly batten. Run it from a pig tail power cable with a male plug only on the end. As you don?t have a Fly Loft, just attach the board or wood suspended on  a cord/rope fed thru a single pulley & anchored off stage, The power cable can be taped or held to the dropper cord by plastic tues & plug into a General Purpose Outlet off stage. With the pendant light cable make it long enough, so the Rose & Pull Switch gubins on the board, is masked by the boarders.
As the Pull cord is pulled in a downward motion to switch on or off, I doubt if there would be any adverse sideways sway movement, if there is, just bridal it of off or to the nearest fixing point in order to tether it.
If your wiring up yourself, just ensure that the light fitting switches On in the Active [if it is a single pole switch]. Unless the light can be physically come into contact of a person standing on the stage &/or has metallic fittings exposed, it would not be deemed as an Earthen situation, therefore it is not requiring to be Earthed,. However it is a good theatre practice to Earth it some how anyway!
This will make it a prac light you can move into a siutable position.

Gieat idea g'?donya Topper!
The ceiling sweep fan rod is a good idea, this would stabilise the fitting. If the unit can be secured to a stable fixture.
From memory the space Aimee uses is a Theanasium [Gymeatre] so this might be restrictive in use a fly batten as I suggested!
If there is only ceiling they possibly utilise the hanging sweep fan fittings, as you suggested, & these could be used on the ceiling, as they come with a shroud rose which is adjusted to the ceiling to tidy up all the attaching.
Also I should have realised with the pull switch the pull switch, must be separate to the incandescent globe fitting, to relieve any adverse weight on the pendant light fitting, when switching. Of course it may not apply your wiring rules  there. Therefore you may be able to purchase the pull switch & globe assembly, as a single unit!
However I must stress that it would be safe to this fitted by a licensed or qualified electrician, in line with local regulations &/or policy!
Also if an actual metallic chain is used, it would be an Earthen situation. Although it may not be practice &/or requirement there, to use an Earth wire, with pressures over 32VAC as it is here. It is a good stage/theatre practice to have an Earthed power supply & Earth continuity on all fittings & appliances [unless they are ?Double Insulated?] for Life safety reasons!

Blimey Aimee 10? Pros width - fantastic!
So I guess that the baine maries are the stage, with the kitchen upstage & the proscenium arch ,is the servery hatch?
"Ah yes I remember it well!" the halcyon days of Cafeatres.
Although you are doing well to have a Caf?torium, much more   salubrious!
Just ensure they don?t turn the Baine Maries On, especially if is a wet one, it could get a bit steamy!
You must have the Old ?Sunset Row? dimmers backsragw?
Although being a bank of 15, that would be a monster! I?d say they might be the more modem 1940?s, wire wound Rheostats, with the jamable sliders?
Now if your Baine Marie stage, is the wet type, with separate water divisions. It could always be utilised as a multi pot ?Salt Water Dimmer?!
You would broil a few warm props & Barbecue the Operator - But the performance would be really cooking!
{Disclaimer: Do not try this in theatre or at home! The procedure is highly dangerous to health & is lethal! Further more Insurance coverage would be with drawn & payouts negated!}