I don't think you need to replace all of the fets but i think you need to replace or add more capacitors. if they have dried out then their esr has increased and the over voltage spikes at turn off may be exceeding the avalanche voltage of the fets, which leads to increased heat losses, and or failure.
but you need a good oscope to look at the actual drain to source voltage at turn off to determine if this is a problem. alternatively you could add an appropriate capacitor as close as you can to the dc bus at each H bridge.
the fets you installed are 55v 8mOhm, stock units are 75v 1.5-1.8mOhm. however, the 3705 has far less gate capacitance than the other units so you might be better off replacing each 4368 fet with 3x3705 fets.
given that the same h bridge failed again, you could have a failing gate driver that is not driving the gates hard enough, the 3705 is able to turn on at a lower voltage than the 4368...
btw, you don't have an H bridge, you have a push-pull topology. when one fet turns on, the other one has double the supply voltage delivered to it, through the transformer. 55v rated fets are probably not adequate for a 24v inverter.
there is also the possibility though i consider it unlikely, that you have a two switch forward converter. anyhow, need an oscope to trouble shoot why just that one section is failing.
if its a push pull topology, the +24v battery wire goes to the transformer (almost certainly through a fuse mounted on the board), two leads from the transformer go to both drains of the fets, the sources are tied to ground.
there is probably a resistor and a capacitor in series connected in series from one fet's drain to the other. check to see that the resistor or the capacitor hasn't burned up.