Forum: Regarding the moving company

We moved from Basel to Lausanne and hired a moving company Classic Umzuege. The contract was to pack, transport and unpack everything, and also had to remove and discard one wardrobe from our Basel apartment. The move was chaotic, they didn't care for cleaning, damaged some furniture, lost one part of our light/fan, took one day more than promised, left 26 boxed unopened, did not remove the wardrobe. The total price in the contract was 4168 chf, and the remaining amount to pay is 600 chf. I told them I don't want to pay for the work that was not done but they're insisting me to pay full 600 CHF. I requested to at least remove the price of the wardrobe removal (171 CHF), but they want to remove this price only if I do the agreement not to claim my damages, and will not write anything on the social media or google reviews. Could you please recommend what I should do in this case:
Should I pay 600 CHF and give my bad reviews on google and stay calm.
Or I pay 600 CHF and complain in some judiciary department? I don't want to pay large fees of lawyers as the money involved is not that big. At the same time I don't want to leave them like this to behave the same with others.
Thank you for your suggestions in advance!
Best regards
Ansar