Sorry to say, but I'm gaoing to disagree with almost everything that's been said here.
there's a lot of bunkum out there to work out your 'fat burning zones'. Ignore. First thing is to work out your maximum, so sprint up a hill several times and write down the biggest number you see
If you do it properly, you'll only (be able to) do it once (last time I did it was 2003)! But this number is of great importance. The best way I've seen of doing it is this:
- find a longish hill
- start going up it fairly hard
- as you get up it, keep pushing harder
- about 100meers from the top get out of the saddle and sprint for all you're worth
- you should get tunnel vision, but when your HRM (heart rate monitor) tells you what your max HR is, that'll be about 1 or 2 beats off.
If you want to get good at doing silly distances like 24 hour events, you need to train your body to deal with this sort of thing. This means that you want to be doing at least one very long ride a weekend. My training for a 12 hour will have me doing about 9 hour rides with something to spare the week before.
Your body will be more effective at dealing with these distances if you only tax your body with these long distance sets. Don't sprint for lights, don't accelerate/brake, don't sprint up hills then free wheel down the other side. I'd also say that you shouldn't be spending time sat at controls, meals and drinks should be picked up and food eaten on the go. You've gotta be riding at 65-75% max HR without going above and also without going below ideally.
I should say that the above is idealised as you're not used to these sorts of conditions so it'll kill you on the 600. This is the advice that should be given to people who've got more time to prepare.
Re-reading your original post, it seems that you've got lots of rides planned where you can do this sort of thing. Be a slave to your HR though. Group riding is only great if they're doing what you want to do.
To get faster over distance, you want to be doing some lactate threshold stuff. Short TTs are great for this. Efforts at 90% maxHR for over 5 minutes are great. Riding with much faster people is also ideal. Sprinting (from lights) is not. I'd question if spinning is really what's best as I don't think the hard bits are long enough from memory.
Yoga will probably help you greatly as being crouched over your bike for 24 hours will be agony on an untrained core. Again, this probably needs more than a month. See if you can focus on stomach and back muscles.
Ignore the swimming, now is not the time to cross train. Leave that till the winter.
If you can't hold a pace for the commute then treat the entire thing as a recovery ride. You should be going very slowly. Any sign of overtraining and things will be VERY bad.
If it was me, and I was in your situation I would do:
Mon - recovery ride commute and an hour of chasing fast people around your local park
Tue - recovery ride commute and yoga
Wed - recovery ride commute and an hour of chasing fast people around your local park
Th - recovery ride commute and yoga
Fri - rest day - take the bus/train/anything but the bike
Sat - Long ride at 70-75% max HR
Sun - Rest day
NB1 - TTs are great instead of the park sessions
NB2 - Move the entire plan down one line if that suits you better, but do the Friday session on Monday in that case.