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Hi Brad, I'm Mike G and I'll be assisting you. Do you have a 2 wire voltage tester?
You'll need to test lug to lug for voltage. I suspect a voltage drop causing an increase in amperage on the circuits. It will be on one leg common to all the breakers that trip. Test as follows and let me know the readings.
1 to 2
2 to 3
3 to 1
Then test each to ground.
Turn off all the breaker and retest. The low voltage reading is as expected. Either L2 or L3 has a bad connection ahead of it. The low voltage is definately your problem. Might want to check the main for the panel feeder. It may be just a loose connection.
You have a main lug panel. There has to be a main breaker ahead of it. Need to check terminations and the breaker.
Test the connections at the main breaker with everything on. Need to find the cause of the low voltage reading.
The low reading a d the comment about Summer being more of a problem, makes a bad connection most likely. Now it may make and break depending on load and tempature. Low voltage = high amperage. That's what trips a breaker.