Gmail – Where Are the Canned Responses in the New Format?

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.

There is not. But depending on your browser's settings for saving forms, you might be able to autocomplete your subject lines.

You can use this form to send feature suggestions for Canned Responses.