HCW,
Your floor heat boiler is a copper tube-fin boiler. Basically, multiple copper pipes are bundled side-by-side above the burner, creating a large instantaneous heater. When the burner fires there must be significant flow through the tube bundle to heat the liquid without producing steam. The vibration, squealing, banging, and other noises you hear indicate insufficient flow through the boiler.
One of the boiler’s safety controls is an automatic High Limit switch. When the liquid temperature reaches the HL, the switch opens, turning off power to the gas valve. The heated liquid exits the boiler and cold liquid takes it’s place…the cooled HL closes, turning on the burner and the process repeats. This is most likely the reason for the burner's short cycling.
The first thing to do is lower the set point of the High Limit...for your safety, the boiler should not be allowed to exceed 120 degrees during testing/balancing. Also, 180 degrees may exceed the floor tubing’s rating. Regardless, 180 is excessive and potentially dangerous…180 is the HL for copper-fin baseboard or radiators used in a space-heating.
Now, look at the copper supply and return manifolds. Is there a pipe and valve connecting the two manifolds? Is the valve closed or open? If closed, open it fully. This is the by-pass which is intended to increase flow through the boiler while also tempering the liquid passing through the tube bundle. Constantly supplying the boiler with very cold liquid creates a tremendous amount of expansion and contraction of the tube bundle. It also keeps the flue gases cool which causes condensation. Condensation mixed with combustion gases creates acidic liquid which drips onto the tube bundle and burner tray. This is not good!
Once you’ve lowered the temperature and restored the primary loop you can now start to balance the floor loops. Close all but 3 or 4 of the ball valves on the manifold and monitor the return temperatures of those that remain open. Once the return loops start seeing increased temperatures, you can start the arduous process of opening more loops to the system. Arduous because the adjustments might take many hours to achieve balance. Did I mention how difficult ball valves are to adjust?