It wont let you choose your sidebar shown, but Dynamic Widgets plugin will let you show specific widgets for certain pages.
What I did was take a page template that I liked, then made a copy of it and renamed it. Then I created a copy of the sidebar (and registered it with functions.php). Then, in the template copy, under sidebar, I swapped out the listed sidebar for my custom sidebar. Done. This way, you can have a page template with a different sidebar. Not sure if this is the ‘proper’ way of doing things, but it worked for me. Good luck.
Thank you @hkcharlie and @frostdawn. Both are good to know. Frostdawn, I’m going to try the method you did. Cool : )