Outlook 2007: Can the From address be different from the SMTP address it is sent through?

Question

Among my numerous email addresses, I have a web-only-based email address which I want to use when writing FROM Outlook 2007. This web-based email address doesn't have an SMTP server I can send through. So, I will need to send it via one of my other SMTP servers, like a gmail one. However, when I do that, most recipients will see the (web-based) REPLY-TO address, AND the SMTP account email address. This I don't want.

So effectively I cannot send an email from within Outlook 2007 that really appears to be sent from my web-based email address. I want the people I write to to only see the web-based email address I'm using/writing from. Eudora Pro used to do it with no problems.

I can manually invoke/display the "FROM" field, and enter my web-based email address there, however Outlook appears to ignore that and still list the SMTP account email address as the FROM address once the email is sent

I am running Windows XP and Outlook 2007 (without Exchange).

I used to be a Eudora Pro user, and Eudora happily sent emails via any legit SMTP server (with my appropriate login credentials) while listing the From address as anything I chose. In other words, it did not differentiate between the Reply-To and the From address.

Is there a way to make that happen in Outlook? I've exhausted researching this on the web, am hoping someone else figured this out. Thanks much!

Note - this is not about maliciously spoofing an email address. All I want to do is write an email in Outlook that arrives as sent via my web-based account - so that the recipient only has that web-based email address from me