I'll chime in with some of my discoveries. I had a weird volume issue with my first 920. I exchanged it, and my new one does the wonderful locking up, but only every 3-4 days. Since this phone likes to lock up when left on the charger, I have been experimenting with different charging times and watching battery life. On to what I have learned.
I installed battery sense on this phone, and uninstalled it to try to eliminate the locking up. When I uninstalled it, I realized my battery actually lasted much longer. So, my experience tells me, the battery apps while nice, they do chip away at your battery.
Also, I installed bringcast to catch one of my favorite podcast that I can't get through the marketplace. This app sucked my battery dry. Like 10% an hour or more while idling. The app is allowed to run in the background, and the phone won't let you control it (under the advanced section of background tasks). There may have been a setting in the app that I missed to solve this. Once I realized how it drained my battery, I uninstalled it.
Last thing here. I worked a night shift last night, and to start the night off my phone was losing battery life quite quickly. It lost 15% in less than 2 hours, with very little usage. The strange thing is, it didn't act up yesterday. Well, I ended up charging my phone fully while I was driving. I took it off the charger at about 9 PM, and a little while later, it locked up a little differently than usual. I did a soft reset, and since then, it has been fine. The phone is currently at 42%, and I'm typing this long message on it. Honestly, I'm amazed at the life I can get out of my phone. One day I had my Bluetooth headset on standby for 8 hrs, I talked for a little over an hour during that time, I played about 15 minutes of games during the day, when I got home I used my phone like normal (surfing the web, reading WP Central

, and playing games) and I went to bed with over 40% battery left. I'd say don't be afraid to experiment. Check the advanced menu in the background tasks area, and try to eliminate the pigs that are unnecessary. Also, you mentioned that your phone gets really hot. Whatever is causing that, is more than likely the culprit, more than anything. That heat is just wasted energy. Hopefully the new phone will serve you much better.