one thing i know works well is what HOI said, but i would tend to use the same tree for the foot ends of the hammocks, & two trees for the head ends.
the distance between the two trees at the head end could be any thing from a double tree to two trees several feet apart.
the distance apart would be something you would just have to experiment with & see what suits you best.
one large tree w/ hammock supports on both sides like you mentioned might work fine too if it doesn't put you too close so that you feel squished.
the spreader bar would probably work fine too. i'd be tempted to post an email to dave on the yahoo group & ask him for details on his experiments.
the spreader bar might be closer to what you'd call "load bearing" than you think. i believe it would be under a fair amount of stress holding two occupied hammocks apart. but the walking cane or pole would probably do the job.
you would just need some well made attachments to add to the hammock supports to hold the ends of the spreader bar.
the spreader attachments on my hammock aren't under nearly that much stress because they are just holding the hammock open. but i made them out of webbing. something similar could probably be done for your support spreaders.