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I am in the design phase of installing a DHW and home heating system
via solar hot water. In the summer the system will produce a lot of
excess heat that I won't be able to use, so I am faced with either
creating a heat dump, or finding a use for the heat.

I was wondering, would it be possible to use hot water to power a
stirlining engine strong enough to circulate water through a pool filter?

Would it be possible? Maybe. Would it be easy? No.
The temperature of the solar heated water is not high enought to operate a Stirling engine with the output needed to circulate swimming pool water through a filter at the rate required if at all.