Sorry for re-opening an old unanswered thread but thought I'd share my solution to this problem. Whilst resizing without moving can be achieved using the suggested solutions in this thread, this does have some caveats as you have found.
I've an alternative solution, again not through tableau directly, but instead I've created a script which can modify the XML of the tableau dashboard to resize everything. I've published a guide a while ago on these forums:
Hope this helps you or anyone who finds this thread at a later date.
Attached is a superstore example.
I took the Region filter (found tiled in the original Overview” dashboard) and messed with that. On Overview(2) I inserted a calc like the one I described earlier (see ), and I used it on a new sheet called “Pop out Region Filter”. I floated the region filter. I made a new floating container, and I dragged the Pop out sheet plus the filter into that container. If you are in the “Designer” group, it will work right off the bat for you. If not, just modify the calc to include whatever group you are in. Then you can mess with the Test Param that is also floating on the sheet to see how it works on dashboard (2). (Obviously you’re not going to have text param on the dashboard when you finally publish it!)
Now go to Dashboard (3). Here I positioned the pop-out container to the left, starting in negative space. Now when you have test param set to “a”, you see it on the left edge of the dashboard. Set it to “b” and it goes away.
For kicks, go to Dashboard (4). I made a copy of the Pop out region filter sheet, and reshaped the mark to be tall and very skinny. Play with test param on dashboard 4. You’ll see the region filter appear to pop into the space it occupied on the original dashboard. The skinny pop-out sheet is invisible to the user. The one cost is that if your dashboard requires cursor access to the area that is covered by the pop out container (in this case “Quantity 34,310), the pop out sheet (even though it is tiny skinny) precludes that cursor access. That’s the difficulty with doing this sort of thing on a tiled dashboard.