"What constitutes a "valid" Brexit, and how important is it to achieve if the price is economically damaging?"
One that restores control over our borders, laws, money and trade. The Chequers plan does none of that. (Even freedom of movement is mentioned with a proviso that EU citizens will still be free to live and work here - with conditions that will be quietly ditched).
It's important to achieve it because without it the UK will be bound to a declining, moribund, protectionist bloc and the long term economic downside of that will be far greater than anything Brexit will provide. Any short term hit that might (note, "might") arise is the price we must pay for allowing ourselves to be in this ridiculous situation in the first place. It is achievable. Lots of countries (representing about 93% of the world's population) do it.