This is not currently possible with Gmail as it currently exists as you've already figured out. Your most straightforward option is probably to use an e-mail client. You don't want Outlook; how about Thunderbird?

Another option might be using something like Auto Hot Key that would allow you to kick off the process of attaching to a message with just a few keystrokes.

Personally, I think the best option would be to upload these files to any of the many filesharing services out there and include the instructions for downloading the file (usually just a link to a URL) in your canned message.

Short answer

Instead of using POP use email forwarding from your other account to be able to use Filters and Canned Responses in Gmail

Explaination

it can't seem to do auto-replies

I beg to differ.

Make sure Canned Responses is activated:

Then you create a filter for emails that are sent to your old email address:

to:(my.old.address@example.com)

EDIT: Note that this will not work for mails fetched through POP3, only for forwarded messages. If your old account has an auto-forwarding feature, that's the way to go. (The other answer here pointed this out.)

You call the filter, say, Old. Then you select a canned response for that filter. Actually, you don't even need to do that. You can autorespond to these emails just the same just by creating a filter for them.

Look at this screenshot: