A resourcing Form 1116 can only be used to avoid double taxation. If income has not been taxed by the UK it could not possibly be treaty resourced.
Interest income isn't really UK tax free, it's taxed in bands with the first band being 0%, no differently from the personal allowances that both countries allow for general income.
As such, I'm not convinced by your argument that income taxed at 0% cannot be resourced, but I'm open to persuasion. Can you provide a citation that supports your point of view?
Note that the treaty supersedes domestic law in both countries and explicitly provides for the ability to resource certain types of income, so any limitations on resourcing would therefore have to be written into the treaty itself.