I have twice started responses & twice deleted them. Some of your ‘why’ responses for particular colleges (esp Cornell & Columbia, 2 programs I know pretty well) are such a stretch that they sound more like rationalizations than reasons.
Good use of the word ‘quite’:
The Truman School is not exactly unknown in policy circles.
So, if this transfer isn’t being largely driven by prestige, why isn’t GW on your list? Affordability would be good reason- do you have financial constraints? if so, what is your budget? One really, truly important element is that if you are looking at policy and/or environmental and/or international studies, you want to avoid debt at all costs! It is hard to overstate just how poorly paid the early years in all those fields are- and you will almost certainly want a masters, which tends to be expensive (although iirc, the Mizzou public policy program has a +1 year masters).
ps,
Keeping all the most selective (and therefore least likely to accept you) places is fine- IF you only want to transfer if you improve the brand name.