There are at least three Chrome extensions that attempt this same functionality, and all of them must use a separate window because of Chrome's architecture. I think that one of mentioned this limitation/workaround on its store page.

I imagine you may have abandoned Sidewise after no response from the developer, but in case you didn't (or someone else finds this post because of a similar problem), did you check out the "Detect all monitors now" button in the "advanced" settings? I'm no expert, but you didn't mention trying it. I would expect that to solve your problem.

You likewise didn't mention the "Allow Sidewise to unmaximize the dock window" option. You should also make sure this option is checked.

I have two monitors with differing vertical resolutions, and Sidewise works for me as you desire.

This is a duplicate of http://sidewise.userecho.com/topic/173166-tabs-jumping-around-in-position-in-chrome/ If you haven't done so yet, you should go vote for that one

This is a duplicate of http://sidewise.userecho.com/topic/173166-tabs-jumping-around-in-position-in-chrome/ If you haven't done so yet, you should go vote for that one

If you right-click on the row with "Window (xx pages)", you'll see an 'edit title" option.

This is a duplicate of http://sidewise.userecho.com/topic/173166-tabs-jumping-around-in-position-in-chrome/ If you haven't done so yet, you should go vote for that one