Okay, I will tell you , what I would do if I were you in this case...
1) We have to glorify our relationship with them citing our cards , limits and WM if applicable..
2)Need to tell them everyone is getting this offer..
Lastly more importantly
3) Need to ask them to expedite the process of this LTF offer( Not asking them whether I am eligible for this?? kind of....Big No... requesting them to speed up the this LTF offer as if this offer already applies to you...
All the above in nice words... Nothing wrong in having a go at it, if it works works, otherwise nothing to lose excpet for one message and 5 to10 minutes..
All in my humble opinion....