Sounds about exactly right and a legit approach from the UK. And you have the spend in the range that interests them. Paperwork comes through, send it back, credit check (you won't even know), card issued.

Data points people will ask is for how long you had 300k spend (or lets say spend over 125k and over 250k), ie what was it the year before? How many years did you have Plat? Did you actively use Concierge/Travel Services. Did you travel a lot abroad (and use abroad)?