Notwithstanding all the advice you've had about removing insignia from your Navy mess jacket, you might consider trews as an option. Trews (tartan pants) were worn by officers I believe because they were more practical for riding in. (If I'm wrong here I'm sure an avalanche of corrections will follow)

If your mess jacket is white - and you have white in your tartan - it would look amazing.

I haven't seen trews mentioned in discussion threads yet but they would work, where a kilt might not look quite right with a mess jacket.