Sorry for the trouble this is causing! I know that the 1.7 release we're working on includes a performance improvement having to do with switching between project and context views. That should help.
As for the lag in bringing up the quick entry window, I'm not sure exactly what's causing that. I'm sure my archive database includes more than 1500 actions - I've been using OF now for several years - and with the archive open, I still see the Quick Entry window appear in less than a second once I hit the shortcut. I don't have 1500 projects active with their own next actions, though. I'll try setting up a test case like that.
(True, there's a SQL database under the hood, but there's a lot of code that makes sure each of those items haven't hit their due date, applies styles to them, and so forth.)
It would be helpful to know what version of the OS you have installed, and what hardware it's running on. That's one possible factor that may be influencing this.
Probably the best thing you can do is contact the
support ninjas so we can gather more information about the problem.