Change the album from unlisted to public in Google+

Note: the email upload feature was recently removed from Picasa Web Albums. This solution no longer works.

I was able to solve this by using If This Then That (thanks @Cawas) and the email upload feature of Picasaweb. Because Picasaweb albums are shared with Google+ this gives me what I want.

Here's what you need:

1. Turn on the email upload feature of Picasaweb
   1. Sign in to your account at http://picasaweb.google.com/.
   2. Click the gear gear icon icon in the top-right corner and choose Photos settings.
   3. On the General tab, in the "Upload photos by email" section, select the "Allow me to upload photos by email." checkbox.
   4. Enter a "secret word," 6-15 characters long. As you enter this word, an email address appears.
   5. Click the Save changes button.
   6. To email upload your photos, just attach them to an email message and send it to the newly-created address.
2. Create an album in Picasaweb and make it public. I named mine "Instagram".
3. Set up the Instagram to Picasa recipe on IFTTT.com.
   1. Set the email address to send to to be the same one set up in step 1.4.
   2. Set the email subject to be equal to the name of the album created in step 2.
4. Take Instagram photos!

Technically, you just need a recipe that takes from Instagram and sends an email message, but this recipe explains why it works and gives credit to the source.

If you want to get fancy, there are a few triggers you can use on the Instagram channel to only share photos with a particular tag, for instance.

Visit Google Takeout. It’s a service by Google where you can download "all" your data of any Google service. Choose "Google Photos". This should contain all your uploaded images.