Sorry to read this. The Diamond desk is probally not aware of the KLM department 'special reservations' or doesn't have access to them.

LOL, as you do a dummy booking on klm you can see which seats are occupied and sometimes that include EER seats

"their policy is to assign exit rows the day of" is simply incorrect.
90 minutes ago i asked KLM in Amsterdam to put me in 6 EC/EER seats on 6 KLM AMS-MAN, -NRT, -ICN and back operated flights and got the preffered seats 10 minutes later. The flights will take place later this week and in November and December. Did this 40+ times this year. So yes it is possible...only the amount of phonecalls that are needed sometimes

What i will do is make a dummy booking an KLM to have an accurate view of which seats are currently available for that flight.
Call the KLM in Amsterdam and explain the situation (....am DM suppose to get the preffered seats for free but website doesn't recognize me and i still have to pay can i have this and this seat please. I also explain the procedure (only their department 'Special reservations' can gift those seats and a lot of call agents doesn't know how it supposes to work))

Beware, the people at the KLM callcenter in Nederland cannot gift you the seat.
Only 'special reservations' (another department) can do this for them. So they have contact that department to get your the gifted seat. Sometimes they also will check your status (call DAL) and this can take quit some time.

You probally got an uninformed person the 2nd time (and the first rep also wasn't aware of the rules (she had to go to her supervisor))...i got them as well...hang up and call again.
Of course easier said then done for me as i'm Dutch compared to someone from the USA.

After you get the gifted seat you cannot change it (well you can but then you have to pay again) and sometimes planes will change -beware