I'm going to get either one of these
M-Edge cases, or one made to size from KreatedbyKim, they said
this one has the most padding, but there are other styles. The M-Edge will be maybe 1/2" too large on the height, it was originally made for the 300. The KreatedbyKim bag will be custom made to fit exactly the 350, just tell them which one and give them the dimensions.
I have the lighted case by Sony which I love and use at home, but wanted a smaller one for when I take it out and don't need the light attached.