Thanks for all the responses! I appreciate all the help. The reason I don't use claws mail was that I had some problems with it in the past:
1) I couldn't ever get a "unified" view where all my inboxes are under one place (and then broken out by address), all my sent items etc,
2) The spam filter SpamAssassin, while good, only would move stuff to one folder if it detected spam. In thunderbird, I can set up each account to move spam into their own folder and then have an overall spam folder in the unified view.
3) At one point, while trying to get my messages available for offline viewing, it permanently deleted a bunch of emails. Luckily, I restored it from my laptop by simply making sure my laptop did not update before saving those messages. Still, it left a bad taste that (3 years worth!) of the emails could just vanish. I'll admit, this one is probably my fault since I didn't know what I was doing but I consider myself at least a little tech savy and there was absolutely no warning.
4) Even with the addon for the calendar, I wasn't able to hook it up with my gmail account calendar.
5) Most of the people on the mailing list used POP3 instead of IMAP so there was some confusion about how to set those properly. But, when you have a laptop, a smartphone, a computer at your apt, your lab, and your parents house, POP3 just doesn't cut it!
Maybe if I get super tired of waiting, I'll try claws again but 3) and 4) really kind of scared me off and 1) I find really useful.
As to some of the other comments:
1) I don't think rebooting my friends server would help as there are several hundred email accounts there and none of them have complained.
2) Thunderbird checks my email every 5 minutes for my accounts.
3) I do use SSL but that's required by some of my accounts and I really don't feel comfortable dropping it.
4) I've never heard of thunderbird "hardware acceleration". How do I check?
On a side note, compacting the folders helped a little, but sadly, not enough. Again, thank you everyone for your suggestions :-).