So you're claiming that using a VPN makes correlation attacks impossible? Do you have any sources on this? I'd love to read up to better understand your thinking.
(unless you are thinking about high level things, like "lots of traffic" -> "something going on", but tor won't help with that either)
But is an embassy always only "phoning home"?
(and for really secure stuff you will want a channel with constant rate, constant size packets, as others said)
(Though certainly things like packet timing, packet size, etc. might make more thorough analyses harder to escape…)