You might get a better result with the green glengarry as it would be separated from the tartan - and if the overall effective shade of the tartan is lighter than the shade of the green within it then there should be little problem.

I think you are right to avoid the dicing.

Colour is an important part of my designing work and I am fairly sensitive to its effects.

I once was suddenly confronted by an elderly gent in a tartan suit - cross cut trews, jacket, plaid, hat - and the physical shock was quite severe.