Right, I get it. Yes, I think that copper foil EMI tape will help if used as you propose but if it only improves, rather than eradicates the symptom, then you could consider looking into and possibly replacing decoupling caps to take into account the altered nature of the EMI.
As luck would have it, there's a paper on that subject available as a PDF from
HERE which proposes some capacitor-related ways to address this issue. It includes the calculations you'll need to establish any changes required in the values of caps that are already present in the vicinity of the added components.
And please forgive me if you're already au fait with this stuff too, but there's another potentially useful document - on EMI shielding theory - available to download
HERE.
I guess you probably looked at the task from the capacitor angle already so apologies if this is something you've eliminated at an earlier stage in the process.