In the past a lot of the non-refundable rates were "cancel within one day of booking" which meant they could be used for LNF booking, and one had time to cancel if the claim was not approved (or responded to in time).
Now I see less of this wording and instead I see (an example for the Berlin Marriott):
Does this mean I need to cancel today (25 August), or can I also cancel with no charge tomorrow?
Hmmm I have had multiple sucesses when LNF a flexible marriott.com rate vs. a flexible OTA rate even though the cancellation policies was not exactly the same some times up to 72h difference if I recall correctly ...