The PCB layout looks good enough to me for operation at 160MHz
I'd be tempted to use the BFS17 for operation at just 160MHz. I think it will be OK to put ground at the back of the board and 0.5mm board thickness should be fine although with a board this thin you will obviously need to make sure you don't flex it and stress the SMD parts. Once this happens they become intermittent time bombs for later failures.
I would add an extra ground via or two to connect the bottom ground plane to the top ground node but it probably doesn't need this with a BFS17 at 160MHz. I had a look at a few OM345 images and I think the layout is slightly different to yours but it's hard to tell because the components are covered in a coating.
Have you tried to take your broken OM345 apart? Looking at the images online I think the resistors will be printed onto the PCB substrate and the caps and the transistor will be the only conventional SMD parts used.