Sorry for delay with answer. Private build cloud is a solution which can be useful here. It is not exactly "uploading own image to AppVeyor servers", but rather "connecting AppVeyor to own cloud and image".
Right now we re-branding it (will be called BYOС – Bring Your Own Cloud) and adding a lot of automation to make it easy to set up. While we mostly experiment with Ubuntu, we believe it should work with ArchLinux OK.
Please let us know if you are interested in trying it. If yes, what cloud (AWS, Azure or GCE) you prefer? And is your own image created by Packer by any chance?