I think from what I was able to find on my phone it comes to around maybe 350

Sounds right, any time to take a vehicle to a shop you can figure 2-300 for any labor they have to do. Plus generally shops (At least the ones I've been to) will only use dealer or OEM parts, which may run more than your standard duralast replacements.

Are they replacing all the coils? Most likely not all of them are bad at once if its still running somewhat.....