Carl,
Your 'tartan' looks not so bad.
The problem is not 'too much contrast'. It's just that some of the colours are too bright and need to be toned down.
To do this, I advocate against giving an overall wash which would only serves to muddy up the whole setting. What I'd do is go over the existing lines with a toned-down colour and do it as many times you need to reach the desired effect. Using this method, you can keep better track of the contrast between the colours and at the same time, you're giving a slight fuzzy edge between the colours just like on the originals.
My advice to first-time tartan painters is 1 – to be methodical and 2 – keep it simple (not too many colours).
In the case of our Celt, it's NOT strictly speaking a tartan (relating to a family or a clan). It's just an example of traditional (primitive?) weaving using the natural dyes available in that period. There's no need for intricated and complex patterns.
HTH
Quang