I had an accident a couple of yrs ago with an uninsured driver which went through the MIBI.
There were no injuries involved, so that made things quicker, still took about 2yrs though. I was claiming through MIBI directly (via my solicitors), rather than on my comprehensive insurance as my understanding was you couldn't do this & then claim from MIBI, but according to #6 from their FAQ this is not/no longer the case.
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I found my solicitors fustrating to deal with as well, but ultimately you have to let yourself be guided by them (chasing up & hounding as necessary).
Feel free to PM me if you want any specifics.