By the way, a belated welcome to the avast forum.
The maximum that you can upload with an upload link of 256 kbps is about 30Kb of data per second (give or take a kb or two). So the maximum you would be able to upload in one minute is about 1.8Mb.
I say in one minute because that is the default timeout value of Thunderbird 1.5 (it was 45 seconds in earlier versions).
With the outbound mail scanner of avast active the message is delivered very quickly by Thunderbird to avast (inside your system - that's why you see the delivery bar move very quickly). Avast then scans the message and avast takes over the delivery to your mail server rather than Thunderbird, so then you see the delay while avast is actually delivering the message.
The log you posted shows that avast was sending mail blocks from 18:20:04 until 18:21:04 (ie exactly one minute) when the connection was timed out by Thunderbird. It shows that about 1.6Mb of the message was delivered before Thunderbird shut it down.
There are two possible steps to take, one with Thunderbird and the other with avast.
The first step is to increase the timeout connection in Thunderbird. With version 1.5 this can now be done in the Thunderbird interface.
In Thunderbird, from the menu bar select Tools > Options > Advanced > General tab then enter a higher number of seconds in the Connection Timeout box - perhaps 150. Then click OK on that panel. Restart Thunderbird.
For avast, one tweak that could speed up the outbound transmisson of the message blocks by avast to more closely match the way that Thunderbird would send the message blocks:
edit the avast4.ini file in the avast4\data folder.
In the [MailScanner] section add a line:
SendInBlockingMode=1
and save the file, probably best to stop and restart the Mail Scanner.
The Thunderbird change should be enough - the avast change will help a bit.