Fast and cheapest way to get Sid?

Exactly. And the counter was meaning the (5) attempts you get to increase (or decrease) your rank. You can run your (5) free ones, then refresh for another (5) attempts if needed to get into your desired payout bucket.

Sorry if that was unclear.

Bottom line, is if it's 5 or 10 a day, you're fine. It'll take a week max. Don't blow money on shard attempts in Chromiums for a character you can get in a week for essentially free.