Yes, take your time doing this. $10k CL is gonna make it tough. Cycling credit as you suggest might not just get your WoH card closed, Chase could shut down their entire banking relationship with you. It's not worth it.

If it were me, I'd spend no more than 75% of my CL each month. Once or twice over the spending period, I'd pay down the balance mid-month to spend more. I would not cycle the CL every month and I certainly wouldn't do it more than once during any statement period. If you're lucky, Chase might increase your CL with this new level of spending.