speakers are 4 ohm and amp says use minimum 4 ohm speakers.
That's a guide, keep that figure in mind....
Using a multi meter set for ohms set at 20k and connected to speaker outputs of the amp the reading is 34.
does this help?
No, that doesn't give you anything meaningful.
It just seems like this should be easy. By simply switching the wires on the back of the amp I get the desired effect
Do you?
Presumably by connecting a pair of speakers to the same channel.
Now go back to your first sentence.
Your amp wants to 'see' an impedance of 4 ohms on each of its channels.
If you connect two 4 ohm speakers in parallel to the same channel, the amp only sees an impedance of 2 ohms - and that is not good.
If that's how you've been achieving your (unique) objective, then the answer to your next question:
'Is the 2 in 1 Out Bi-Directional Audio Switcher the answer or the Fosi?'
The answer is no.
Like I said, a combination of switches could achieve your objective, but I wouldn't want to encourage you to drive your amp into impedances that are too low for it.