Access OWA via http://servername/exchange

You can perform a redirect to the new address using IIS.

Windows Server 2008 For a Configuration in Which SSL Is Not Required on the Default Web Site or on the OWA Virtual Directory in IIS 7.0

To use IIS Manager to simplify the Outlook Web Access URL Start the Internet Information Services (IIS) Manager snap-in.

Expand the local computer, expand Sites, and then click Default Web Site.

At the bottom of the Default Web Site Home pane, click Features View if this option is not already selected.

In the IIS section, double-click HTTP Redirect.

Click to select the Redirect requests to this destination check box, and then type /owa.

Under Redirect Behavior, click to select the Only redirect requests to content in this directory (not subdirectories) check box.

In the Status code list, click Found (302).

In the Actions pane, click Apply.

For the new settings to take effect, start a command prompt, and then run the IISReset command.

Source

You can also modify the properties of the virtual directory, but I'm not sure of all the consequences of that.

To use the Exchange Management Console to modify the properties on an Outlook Web Access virtual directory In the Exchange Management Console, locate the virtual directory that you want to modify by using the information in step 2 or step 3.

If you are running the Mailbox server role on the computer that is running the Client Access server role, do one of the following:

To modify an Exchange 2007 virtual directory, select Server Configuration, select Client Access, and then click the Outlook Web Access tab. The default Exchange 2007 virtual directory is /owa. To modify a legacy virtual directory, select Server Configuration, select Mailbox, and then click the WebDAV tab. The default legacy virtual directories are as follows: /Public, /Exchweb, /Exchange, and /Exadmin. If you are not running the Mailbox server role on the computer that is running the Client Access server role, select Server Configuration, select Client Access, and then click the Outlook Web Access tab.

In the work pane, select the virtual directory that you want to modify, and then click Properties.

In the virtual directory properties dialog box, select the tab that contains the properties that you want to modify.

Make the changes that you want.

Click OK to save your changes and close the properties window.

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Obviously, read up and apply what fits for your given situation.

Try http://owa.domain.com:443 - that error smells like it's trying to answer with plain HTTP on the HTTPS port, so see if it'll answer you in plaintext.

If that's the case, triple-check the binding config and certificate assignment in IIS on the OWA site.