That's actually not true[1]. You can change status to an E-3 from within the US by filing Form I-129.
That's actually not true[1]. You can change status to an E-3 from within the US by filing Form I-129.
This can be a big deal. I changed from L1B to L1A to H1B (without leaving the country) then when I wanted to leave the country the legal advice that I received (IANAL - TIJAA[1]) was that to be safe I should return to my home country to get the new visa stamp, the Vancouver embassy might legitimately decide not to apply it - at which point I'd be stuck in Canada needing a plane ticket to the UK in a hurry and have the possibility of a multi-week wait for an appointment at the London embassy...
I waited on my green-card application to get to the point at which I could get an Advanced Parole[2] document and traveled on that instead, but this did mean: a) several years in which I couldn't travel outside the US; b) repeated lectures from border officials that the AP document was for "serious travel" only and that snowboarding trips to Whistler didn't count.
YMMV
[1] This Is Just An Anecdote [2] http://en.wikipedia.org/wiki/Advance_parole
http://www.gpo.gov/fdsys/pkg/CFR-2010-title22-vol1/xml/CFR-2...
Others have been done much quicker but I would be prepared to wait going this route, and also take USCIS's processing times with a grain of salt.
If the E-3 allowed for premium processing[1], portability[2] or the 240-day rule[3], I would try I-129 again otherwise I think I'll just apply for a new visa outside the US.
1: Pay an extra ~$1200 to hear back from USCIS in ~2 weeks.
2: Permission to start work for a new employer upon filing the I-129.
3: A 240 day grace period during which you may continue to work for your existing employer after your status expires.