This is the sort of situation where perseverance might be beneficial, and where it might be worth reading the fine print of your contract. Talk to your insurance agent, too, not the guys on the claim line. There's a line of robotic if-then statements that drives most insurance and the ability to slap the pinball machine, tilt it and get a human draw again is useful. I'll bet that your insurance agent can figure out the verbiage that your contractor needs to write on the estimate in order to have the claim be valid. I would expect that 300 gallons a day at ten below freezing might substantially contribute to frost heave, which might be extraordinarily detrimental to your foundation... and as the remedy is comprehensive, you might win.

For example, yesterday I got a nasty-gram from my health insurance. They want twelve (12!) pieces of documentation related to the time a choad in a limo swatted me across the 405. Which was in 2014, and which I received no injuries from. But I had to explain to them that I'd sustained no injuries, that my medical claim was an urgent-care physical exam to ensure that my instincts that I was unharmed were correct, and that no insurance company had paid a dime on any injury related to the accident including them. They then told me that in order to bypass the 12 pieces of documentation, I had to write a human-parseable letter explaining this fact.

So in the end, I got a letter asking for 12 pieces of documentation that I was (hopefully) able to banish with half an hour on hold and a 3 paragraph email. But up until that point, it was kafka-esque.