Hi, eulloa24,
A lot is going to depend upon what you have your hearts set on what you want to see and do. You'll need to get an early start on your first day. If you really want to visit Stirling Castle, you could possibly visit it on your way to the Cairngorms. It's not too far out of the way. If you take an hour or two to visit the castle, you'd need to skip one of your outings on the way north.
Is the bungee jumping which you're referring to the one at Killiecrankie? That's a long way from Cairngorm National Park. But it's on the way north, off the A9, so it's not out of the way.
As far as the Reindeer Centre goes, it appears that they only do one hill trip per day in October, and that starts at 11:00 a.m., with a recommended arrival time of 10:00 a.m.. So if you have your hearts set on that, that will pretty much scotch (sorry!) your plans for the bungee jump, unless you want to double back. Plus the hill trips need to be booked in advance.
You don't get to see much of Loch Ness from the A82, so you may want to forgo driving up to Inverness. Instead, you could double back from Aviemore or Killiecrankie, and take the A86 or A889/A86 (depending upon where you're coming from) to the A82 at Spean Bridge, and spend the night in Fort William. That would give you an earlier start the following day to get out to Glenfinnan. If you don't specifically need to see the train crossing the viaduct, you could get on your way all the earlier. That does eliminate Urquhart Castle, but with your limited amount of time, something's gotta give!
With that earlier start, you'll have enough time to visit Glencoe, and if you decide not to take that short hike, you should have enough time to visit Stirling Castle on the way back to Edinburgh. If you get to the castle after closing, you can still walk around the exterior, and I believe the cemetery as well. It shouldn't get dark until after 6:00 p.m.
I hope that that has given you some more ideas for your planning. If you decide to stay in Fort William, there are plenty of places to eat and sleep. It's also a mountaineering town, as it's near Ben Nevis and other mountains, as well as Glen Nevis, a popular hiking area.
Whatever you decide to do, have a wonderful time in Scotland! I truly wish that you had more time, but this adventure will no doubt whet your appetites for a (longer) return visit!
Very best wishes,
Mike (Auchterless)