I've never built one but here's some thoughts.
1 The saddle idea around the tree sounds good. There are high-grade swing set seats which are made kind of like a tire, although not as tough. They come with grommets in the end so you could bolt two together to get a good circumference and they're made for good sized loads - although the company lawyers would most likely never approve it for this use. Too many lawyers in this litigious society
2 Another method of attachment which I recently used on a leaning tree with a 20" diameter trunk. I drilled a 1.25" hole right through the thickest part of the tree where the main horizontal branches begin. I took a piece of all-thread and slipped it inside a poly tube - I imagine electrical tape with tape sealant could have worked - the idea was to allow the tree to grow back around it without getting rust on the all-thread and weakening it.
I put a plate on each end with an 'angle adjuster' - a piece of steel pipe cut at the angle of the tree at the penetration - the other a straight cut so the fastening nuts would bite squarely on the all-thread, since the trunk was not a perfect cylinder. I welded a half circle of rebar on one plate to attach my steel cables to. I got mine at Harbor Freight and they were galvanized - I've also seen it called aircraft cable. Rated at 4000 pounds. There's plenty of cable and pulley companies out there. I'd rather use pro stuff than big-box products, but it's your project.
3 - You are really creating something potentially quite dangerous - particularly if alcohol is involved - when people think they're smarter, funnier, better looking - and daring. I was at a party with a zip line which went from the house, over the pool and attached to a massive eucalyptus tree trunk. It was built by an engineer, so there was no structural concern . . . . however, since the idea was to release over the deep end of the pool it could be lots of fun.
Except for one drunken fool who released too late - and I wince at this part - his legs were spread apart and he landed with his crotch squarely on the concrete edge of the pool. I had a straight on view along the edge of the pool and a number of we males who saw it from that angle collectively bent over, grabbed our crotches and made all sorts of painful noises in unison.
The drunk had no idea what happened and was taken to the ER. Fortunately, he broke nothing, walked funny for a month and had the mother of all bruises. He'll probably never need a vasectomy.
So that's all - but since I've been a pool and landscape contractor for 43 years, I get called in as an expert witness on all manner of outdoor injuries. There's a lot of them caused by crappy construction, maintenance and alcohol-enhanced temporary testosterone.
Good Luck