Try holding shift as you start the affected apps - this drops some of their memory of their last session (eg, Safari forgets the tabs you had opened, instead of trying to reload them).
Failing that, a permissions issue is still a strong possibility, but since the issue doesn't occur in a new user account (indicating the fault is in your main home folder) and Disk Utility's "repair permissions" function only affects system files (as opposed to anything in a home folder...), you may need to try correcting them manually.
If you Get Info on your home folder (highlight it in Finder and hit Cmd + I), down the bottom is a Sharing & Permissions section. You need to make sure your account is listed there - it should specifically say "(Me)" after it - and that the privilege level next to it is Read & Write. The other users / groups listed don't matter so much, but should be set to Read Only.
Assuming that all checks out, there's a button at the very bottom of the panel that looks like a cog, which should have an option to "Apply to enclosed items". That takes a while to complete (a few minutes, usually less than a dozen), but once it's done, reboot and see how things go.
You may need to click the little padlock in the lower-right and enter your password before you can make changes.
