Contractor dispute. Looking for an arbiter in Connecticut.

[Stephen R.]

My home improvement contractor quit just as I was about to fire him. He originally quoted me 6 weeks for project completion, we're currently at 11. The backup contractor told me he's going to need another 5 weeks to finish. 

My contract includes a clause entitling me to liquidated damages ($2,000) in the event of a breach but I'd also like to recover the last payment ($4,000) that was made, specifically, for the purchase of materials. CT law limits small claims to $5,000 but I think an independent arbiter may be faster and cheaper. 

I'm looking for recommendations as I've never been down this road before.