Are there any effective alternatives to the traditional lighting?
Set your standard lighting up as an isolated studio in a corner of the hall, or in another room nearby. You will need a "wrangler" to go out into the crowd and gather up suitable pairings, groups, etc. and bring them to you. Ideally, you want two of them, one from each family, since they know what the logical groupings are.
Choose a nice available background, or bring your own.
You also need a mobile rig. I've gotten a lot of mileage out of a flash bracket and some kind of diffuser, with the flash dialed back to act only as a fill for the available light.
Perhaps counterintuitively, this means you use more power outdoors than indoors, because outdoors you are competing with the sun. Indoors, you might be setting FEC -2 or -3 for TTL metering, or setting the flash on manual at 1/64 power. This may help with your battery situation.
Cannot use a flash as it runs out of battery even with a powerpack. We cannot take risks of changing the flash batteries on field during the event.
That seems like quite a bold statement to run unchallenged.
Why can't you take a risk? You were under the impression that everything was under your control?
What is this risk, anyway? That you will get 3,599 properly-exposed photos to sort through instead of 3,600?
Shooting a live event is like surfing. A skilled surfer knows how to look out over the ocean and see the wave long before it crests, put himself in its way, and ride it until it disappears. Then he goes out and finds another wave to ride. A surfer doesn't get to ride every wave; he just makes the most out of the ones he does catch.
If your clients are demanding that every instant of every angle of every person be recorded for perfect replay, but that you accomplish this while remaining perfectly invisible, you probably need to fire your client. They're not going to be happy with anything you produce.
If instead this "requirement" to shoot so many shots that you drain multiple power packs and balk at the time it takes to change even once is coming from within, your client is probably right: you are causing a nuisance at the wedding, not blending into the background as is proper. The wedding is not about you.
Minimising lights to one unit where sungun and strobe be used on a single stand.
Single-source light is what you use for dramatic art pics. Chiaroscuro kind of stuff. It is not what you want for portraiture.
If you absolutely cannot have a second light, at the very least allow yourself some kind of bounce. Use a background stand to hold some muslins, or tape the muslins to a nearby wall, or get an intern to hold up a large light disc so as to bounce the main light back to the other side of the subjects.
If your posted venue photo is accurate, trying to use room lighting as your fill is going to create a color temperature mess. You'll have bluish flash/strobe light on one side of your subjects' faces, and dark yellow light on the other. Yuck.