I used (and liked) Jott back when it was free and I can totally understand getting hooked on the service. It used to remind me of Wildfire which I always admired. And their corny MP3 demo, which ain't as admirable. Agreed that Dragon is not the right direction, and that Jott has some amazing productivity features you're not likely to duplicate. I was thinking about a few oddball alternatives, but none of these are nearly as slick and are mostly for requirement #4 (the easy one.) Listed from best to worst:

• Remember The Milk is a nice way to post notes to yourself. You can subscribe to your notes via an RSS feed, there are iPhone/android clients, a web site, and here's a hack integrating with other services that could also meet your needs.
• Android I have a pal who uses voice to text on his Droid for a lot of stuff. The transcription isn't all that great, especially when compared to humans. But I think you could do many of the items you've listed with spoken "verbs" (e.g. "Navigate" "Call" etc.) followed by spoken text.
• Google Voice turns voice messages into text automatically, and then you're sent an email transcript. You could map your Google voice number to your office phone, and then not pick it up.
• Ooma provides a subscription "voice mail to text" service with actual humans that listen and transcribe the call. So you could call home (but that might wake up your family) and leave a message. Also, of course, you'd need to buy an Ooma box.

Hope that helps,

Robert