There's no simple way. There are I think a couple very strange ways.
One that springs to mind is to use a couple Gate modules and apply autoRun a little cleverly.
Gate is a relatively new Sideview module, and it has two features. The first allows it to block pushes from upstream until some set of $foo$ tokens are present. The second allows it to kind of teleport pushes from it's location the module hierarchy to another Gate module elsewhere in the hierarchy. Here we will use the second feature only.
You could have your form element modules, and then downstream from them you have a Gate module with an "id" param of "insideFormElements". Then downstream from the Gate you have your tables and charts and whatnot.
Then, completely unrelated to those modules, up at the root level of the view you could have a SavedSearch module with a Gate module downstream. That Gate module would have a "to" param set to "insideFormElements". Put an autoRun="True" on the SavedSearch module and nowhere else and you've basically implemented the thing you need here.
When the page loads, the SavedSearch gets the scheduled job, and then teleports it through the gate past all the form search elements. Then when the user makes really any change in the set of form elements, that push would clobber the old push from the saved search results and you'd get an ad-hoc search dispatched automatically.
Use cases for the Gate module are always kind of brainbending, but it's an extremely handy module if used wisely.
As always the docs and the working examples for the Gate module are embedded in the Sideview Utils app itself. Gate released in 2.4.8 but it received pretty substantial changes in later releases so make sure you're on the most current Sideview Utils (2.7.1 as of this writing).
http://sideviewapps.com/apps/sideview-utils
UPDATE: Actually the Gate module idea doesn't work here, due to a wrinkle around autoRun="True". Pulldown modules need an autoRun="True" attribute somewhere upstream from them in order to render themselves when the page loads. However once you put that autoRun="true" attribute it will push on down through the rest of the page and your scheduled search results wont be used - instead the autoRun push will dispatch an ad-hoc search. Sorry for the waste of time!
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