Phasing a biamp system

Use a tone generator and sound pressure meter.  There are multiple tone generators you can download.

I have several lab quality frequency generators and SPL meters. Could you explain the process that you are recommending?

My thoughts are that you don't understand how to integrate speakers.

While you can test polarity using a 1.5 to 9V battery it may not yield the correct electro acoustic integration of the two sections.

If you have speakers designed to be biamped, and you are not using a line level crossover simply assume the speaker's inputs are correct.

You can use equipment to check phase, but you can actually do it with your EARS just as well. Put your head directly in front of your speaker drivers, turn on and play music or a low level signal near the low midrange or upper bass crossover frequency. Then reverse the speaker leads on the bass OR midrange, you should be able to tell which sound appears to be radiating from between both drivers. It really should be quite obvious. I use this same method for double checking the phase in a tri-amp system as well. Of course you should first set it up with a battery and verify the cone movement of the drivers, but after that it's just your ears that make the decision.

If you have speakers designed to be biamped, and you are not using a line level crossover simply assume the speaker's inputs are correct.

+1
If you bypass all the crossover components then there's a lot more to do along with phasing... BTW in a loudspeaker you're interested in the phase at the crossover frequency, what happens either side of that is of less importance. If that is what you're doing then reverse engineering the crossover is a good start... not quite as difficult as it sounds if you know a bit of basic electronics.

What speakers and amps are you using?