search system

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Now I know where that limitation comes from.
Never wanted to decrease it so I was not concerned.

I think you should abandon this idea of searching for 2 character strings.
It sounds like it will cause the relevancy ranking to go out the window.

And after looking at your website I do not see the need.
There are not that many products to where detailed search is that important.
Adding a bit more local navigation and perhaps some related items links and I doubt users will not be able to find what they need via browsing.

What confuses me is you said it does find the two character strings in the core Joomla search.
Is that correct?

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yes if I enable the content search plugin it will work but it is using SQL like searches not full text searching like flexicontent plugin.

I could change the search plugin to use the same method as the joomla core plugin to use like searches instead might be the only option at this stage.