Heavy Engine P0302, P0304

Hi Prius Experts,

Yesterday, when I started my 2014 Prius V (120k miles), it rattled, and shortly after that, the engine light came on. Today, I took the car to a showroom, and they charged me $189 for a diagnosis (I also called a local garage in Austin, and they quoted $190 as well). The Toyota service center informed me that there are misfires in cylinders 2 and 4, which occur only during initial startup. The codes they provided are P0302 and P0304.
To diagnose the issue further, they are quoting an additional $500.

I would appreciate your advice on how to proceed. I have kept up with all recommended services from Toyota, with the last service performed at 116k miles just a couple of months ago. At that time, Toyota did not mention any urgent issues.

Should I pay the $500 for further diagnosis, or would it be better to consult a local service shop in Austin? If anyone can recommend a reliable Toyota service center in Austin, I would be grateful.

Thank you!

 

Thanks @rjparker for the references. Before contacting the dealer, I called Bearden Automotive, and their price was the same. As a result, I decided to go with the dealer. I'll also be getting a quote from Hometown Hybrids. However, I am likely going to skip the additional $500 fee to the dealer and take my vehicle to Bearden Automotive for further diagnosis.