Give the 'find' window a separate context for each tab

Frequently, I want to simultaneously jump through the occurrences of a searched-for string or regex (via the find window at the bottom of the screen) in one tab, while jumping through the occurrences of a *different* searched-for string or regex in another tab.  Currently, this is a big hassle, since the 'find' window has a single context that is shared among all tabs.

For concrete example, suppose I have Tab 1 and Tab 2 open.  In Tab 1, I want to walk through the occurrences of the string 'foo', and in Tab 2, I want to walk through the occurrences of the string 'bar':

1. I use the 'find' window at the bottom to find 'foo' in Tab 1.
   
2. I switch to Tab 2, and use the 'find' window at the bottom to find 'bar'.
   
3. I switch back to Tab 1, and want to move to the next occurrence of 'foo'.  If I use the 'find next' action, instead of moving to the next occurrence of 'foo', I move to the next occurrence of 'bar' in Tab 1!  Instead, I have to type my search query (the string 'foo') again.
4. I switch back to Tab 2, and the same issue occurs.