I am glad to tell you that all the things you'd like to see in the leagues section are there! Well almost .. or, they will be.
Concerning timezones, you can always simply write in your local time and the site will convert it to UTC for storage, automatically. And then other people will see your time in their local time again. So all times (on this whole website) are always local. When you hover over any time on this site, you'll see a tooltip with the UTC time.
The calendar has links to the leagues / seasons / race info and those pages have their own info links again, with LFS join links (if the server is online). There will be the option of season / round signups, for single racers or multiple. In fact, the league admin can set whatever requirements and information he needs himself.
I'm pretty far along with it already, but i still need to finish a few pages and then make it all a bit more user friendly. Then it can go live. The only problem is that I'm completely swamped at the moment and have very little time to work on the site throughout weekdays. This week I've only been able to fix critical bugs and do a few tweaks.
But ... will get there, though it may still take a few weeks. And then a few more weeks to tweak when public feedback comes in.