so wait, you put the missing spacer in and then torqued down the stem cap and then tightened the stem bolts on the steerer, right?! then you grabbed both ends of your handlebars and, with your armpit on top of the saddle and your front brake pressed, you pushed forward and pulled back on the bars and you still have play in the headset?!

i would say to make sure the headset is in good shape, meaning the mechanic at the shop didn't damage anything and that everything is where it's supposed to be. you can easily drop the fork, so do so and look at the headset and where the fork and head tube meet to see for yourself. like someone already said, i wouldn't personally trust a mechanic that said i needed to spend $350 on a fork when they weren't either sure or right about it needing to be replaced. me personally, i would get least 2 more opinions from local shops and i would actually say something to the current mechanic about why he made you spend $350 on a new fork that you didn't really need...