Are there any clever tools or tricks that can be used to automatically [nee quickly] convert (a large amount of) complex polygons into simple polygons i.e. splitting geometry so holes are still represented but are not drawn as holes...... see attached.
I believe so, but this can get complicated by several variables:
To help us answer this:
Chris Donohue, GISP
Hard to now how complex your dataset is, but one option is to add a new temp field, assign unique values to each poly (calc base on the Object ID or similar), then go to the polys you want to combine, and change the field to be the same value. once done, dissolve on that field. Kind of a square-peg-in-round-hole type of editing, but if you can find the polys, might work. if you have thousands, probably not a good solution.
In which case, try lookin and test with Eliminate_management or EliminatePolygonPart_management
I was testing both recently in my program trying to eliminate sliver polygons. I ended up going with the first option for my purposes (sliver polys along boundary after a clip), and although it took a few tests to get the correct Selection set, I have it working in my script (since will run it often).