Your view has to be written using the advanced XML, or converted to the advanced XML, but aside from that it's fairly simple.
In the advanced XML the nesting of module tags inside other module tags looks very confusing at first but this just encodes how modules get information from other modules.
So if a given module is inside a 'TimeRangePicker' module, it will inherit that TimeRangePicker's current time range. And if it's outside it wont know about it.
Furthermore for simple items like the base search string and the timerange, you can also clobber upstream changes by having another deeper module specify those keys again.
So making a change like this amounts to indenting some set of modules on the inside, and adding a new HiddenSearch module with a new timerange that replaces the one from higher up.
[[ the last of the modules you want to operate on the old timerange]]
[[ (newly indented) all modules from here down will operate on the 'last 7 days' timerange]]
The bad news is that it looks like there's no way to set it to All Time. This is more or less because the 'all time' timerange is really the absence of a timerange, and the params on HiddenSearch arent smart enough to know the difference between not wanting to set earliest/latest, and wanting to set it to an explicit null...