I think you're not using the parallel path correctly for your purpose. I would reduce it so only the amps are parallel, then use scenes to change what other blocks are enabled or bypassed, and which amp is enabled or bypassed, and, like
@trixdropd, adjust the blocks so their Bypass Mode is exclusively muting (one or the other), or just put them in series, because the switching is very fast these days.
P. 7 in the Blocks Guide talks about the various modes available.
Alternately, if you want to switch between rows, you can use Mixer or Multiplexer blocks. Mixer lets you blend multiple rows or turn on/off their levels, whereas the Multiplexer lets you select one row from all the available rows. For simple selection of a row the Multiplexer is "more better".
Dig around in the factory presets, or search the Factory Presets page in the Wiki, and you'll find examples of all these things.