UPDATE:
Yay!! So when my 1st statement from the new Marriott Chase card posted, I had a balance of just over $5000. After waiting a few days, I had yet to hear a peep on my 100K MR bonus. I called Chase and was told that they use statements (balances & dates) to determine when or if you qualify for the bonus.
Arrg!! The problem is that $95 of my statement balance was for the annual fee on the credit card, and that annual fee does not count towards the $5000 in qualifying charges. According to their records I charged $4,970.54 during my first statement period and will have to wait for the next statement to qualify. The rep put a note on my account that I needed the points to post to my Marriott account before July 31. I doubt it matters, but did so just in case.
Note: All the MR points (6x) from paying my maintenance fees early did post. I am now at 1,460,000 LT MR points. I'm getting ready to roll over 40k points from DW that I purchased from SPG and converted to Marriott. If the 100K bonus from Chase hits my account in a timely manner, with a statement date of July 20th, I should make the 1.6mil LT Gold requirement before July 31st. I also converted one timeshare to 100k MR points as a safety net. Based on others' experiences those should post in October.