What are acceptable reasons to request a new winner?

ratio doesn't count.

rules like these

View attached image.

If the winner has never made a giveaway and has won over $100 dollars of stuff, is that a valid reason?

no
Edit: i'm too slow

View attached image.

Oh there is a list, lol. I feel stupid now.

Thanks for the pic =)

In addition to that, regarding your last question: They have seven days to activate and mark it as received.

The winner has one week to activate the key.
Oh, and to avoid such scenarios as described above, use levels for GAs.

The only valid reasons for a re-roll are:

1. the winner didn't activate (or regifted) one or more of their wins and/or won the same game multiple times (any game),
   • but the re-roll will be granted ONLY if the infraction happened in the last 30 days, or if it's older but they didn't get suspended for it,
   • mind that winners have 7 days to activate their wins, although they're supposed to mark a game as received only after activating it in the linked Steam account;
2. the winner ignored you for a week,
   • you need to provide proof that you tried to contact them during this time;
3. the winner already owns the won game,
   • this is pretty self-explanatory, and these re-rolls are usually the fastest ones (although some people like to complain about support being slow, thy're just overworked);
4. the winner owns the majority of the items in a package,
   • even ownership of a single item in a 100-items package (just to make an extreme example) entitles giveaway creators to a re-roll request.

"Leeching" is not a valid reasoning for a re-roll, although sometimes, users with hundreds of wins and no (or few) created giveaways "forget" to activate all their wins.
For the next time, if you don't want to reward greedy users who consider this site as just another way to get free games, set a level restriction on your giveaways.
I'd suggest at least 3-4 for better games, as they require a sizable investment to reach.

Just a little precision: you can use the "Regifted or did not activate previous wins this month" even if the infraction is older than a month. As Mike90 said, it will be rejected if it's older AND suspension has already been served. You shouldn't refrain yourself from opening the ticket because of the 'last month' thing, as I've been told by support.