How to fake a “from” address in Thunderbird

I have an e-mail address from a provider which does not provide me with an inbox, only redirection. In other words, all messages sent to that address will simply be redirected to an address I choose. Nor can I send mail from that address.

This is my primary address. It's easy to remember, easy to spell. I want to use it for incoming and outgoing mail.

Previously, I had this set up with Gmail. Mail sent to the address would be redirected to my Gmail address. And, in Gmail, if I replied to that mail, or if I wrote a new message, the From address would be faked to that address. (Gmail would also add a Sender address of my actual Gmail address, so that the messages would not get caught by spam filters.)

I now have moved away from Gmail. I am redirecting my e-mail to a different address: contact@example.net (my own domain).

This is what I want:

1. When I reply to a message in Thunderbird, the From address is set to be the same as the To address, even if that address is a different domain.
2. The Sender address is always set to contact@example.net, to avoid spam filters.
3. No matter what the From address is, the mail is always actually sent from the mail.example.net server, using the login details for the contact@example.net account.
4. To cope with the weirdness of Microsoft Outlook, and the strange ways it behaves when it gets mail with From and Sender addresses, the Reply-To address is always set to be the same as the From address.
5. When I write a new message, not a reply, I should get a choice of From addresses. Ideally, the default would be my non-mailbox address.

This question is closely related to Set Thunderbird "from" address by incoming "to" address, but there are a couple of differences:

1. I have two different domains, and one does not provide mail services, so I need to fake the From address and use a Sender address.
2. I want my default From address to be faked.

This is an IMAP account. Thunderbird is running on Ubuntu 12.04 LTS.