The only way that those amperage readings make any sense to me is if HEAT3 (or LS3) is open and HEAT1 is shorted to ground on the line side. That would leave HEAT2 as the only working element; but it's using the metal housing as the return path instead of being routed to L1 via the HEAT1 coil.
The breaker won't trip until it sees more current than it's rated at. Depending on where the short is the current value on any given phase may not get high enough.
A GFI might do the trick; but only if the return current isn't somehow coming back on one of the phase legs. If this was something expensive I'd suggest a protective relay that would operate if the current on the 3 legs differ from one another.
Since there is no contactor for the third phase, they may be using a corner grounded delta. In that case, the heating element will see the full 400 V across it and the current will be approximately double of the calculated. That comes a bit closer to the measured values.