Seems like a huge overpay, but that's life in today's NBA. The team really had no other choice but to give him a supermax.
		
		
	 
Well they could let him walk and use $304M in other ways.   You telling me there's no other way to build  Jaylen Brown as a combo of two players?  You could find a player that has no left hand, and another that can't shoot.
		
 
		
	 
BOS has been a Final 4 team multiple times in the past few seasons. If they don't have Brown, the chances of them staying in that category drop dramatically. If they didn't extend Brown, all they could do would be to trade him for pennies on the dollar with only one season left on his deal. Whoever acquired him would have to be concerned he wouldn't stick around (and then have to give him a massive contract if he did want to stay). Boston would likely take on a bad contract or two to match contract value and maybe a couple of so so draft picks. Or as you suggest, they could lose him for nothing.
That would derail their title hopes in the short term. Could they reallocate $300+ million over the next 6 years? Sure. Just tell me which two players they should draft or bring in. Boston is not a free agent destination, so I would expect that would not be as easy as you are making it out to be. And the draft picks wouldn't be anywhere near the top of the draft, as they would certainly be protected.
As for swapping Brown for Lillard, Lillard shut that talk down immediately and wanted no part of Boston.  The best option for Boston was to see if they can win with the reconfigured roster. If that doesn't work and Brown still isn't enthusiastic about being a Celtic, they could move him with lots of years on his contract. That would net them more than nothing if he left in free agency and more than if he was a lame duck demanding out with a year on his contract.