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I reckon you might be okay with them. They're not ideal but they have good cornering grip, which is what you need at Somerhill. Most of the course is grassy, but the section from the top of the course to the bottom is where you need grip, a fast descent into a sweeping right hand corner, up the steep bank to the top, which is usually rideable if you get the corner right, then the series of banked bends where grip and technique is key.
What tyres have you currently got?
I may be wrong, but I don't think Somerhill will be a super muddy race. The course can get very muddy, especially on the lower half of the hill, but Southborough CC have evolved the course over the years to stop it being a mudfest (which it was in the first few editions). It's been very dry until this week, and I don't think there's been enough rain to penetrate the soil deep enough to make it properly muddy. It'll more likely be slick on top but firmer underneath so a full mud tyre may be over kill.
As I said though, I could be wrong (there's evidence of my optimism earlier in this thread about a race at Cyclopark where I got it very wrong).