Unlikey to be non-stayers as they are spending 90K 0r 105K on 3 points nights Wed/Thu/Fri in basic (Superior) room, then 3x paid nights Sat/Sun/Mon (Deluxe room) checking out Tuesday.
They expect as Platinums a 1-level upgrade paid nights 4-6 Deluxe->Club with free lounge access as paid nights.

Obviously did not earn 100K points they are spending at IC brand, but could have earned at HI and HIX brands, or if USA nnK's via credit card spend

Saying they won't hang around hotel to swap room from Superior->Deluxe on the Saturday, so wish hotel to give same room for all 6 nights starting Wednesday on arrival.
No problem.. have to pack cases to move anyway, hotel staff will happily move your packed cases to new room in your absence.

Reading between lines, being Platinum with Paid room Sat-Tues, they expect unwaranted upgrade to club and also with free lounge access. With excuse they can't be expected to move room, and so want the initial 3nights basic rooms on points nights upgraded as if they had booked paid Deluxe as for their final nights.

Because nights 4-6 are Deluxe, one below Club, they want 2-level upgrade + club access first 3nights which are NON-QUAL on points, and 1-level upgrade + club access for last three nights.... that is extremely unrealistic and greedy, especially as Platinums at an IC where only platinum entitlement is free internet, + maybe one of the best rooms of the type actually booked.

Best Advice is ....Although no entitlement from IC Miami, if they are a bit humbler, set sights lower, write a nice email asking pretty please, if it would be possible for an upgrade the first 3nights reservation to match the last 3nights booked as paid deluxe, the hotel may (I say may) give a Deluxe for all 6 nights.
IC Hotels will sell Club Lounge access as an addon, if lounge will not be too crowded by doing so. So also ask the price for purchasing Lounge at checkin on the same email.