I know I’m probably to late to the party, but I feel like chipping in since I found this site googling for h-bridges and freewheeling current paths.
I’m currently taking a course in Power Electronics and we have been studying H-bridges, or 4 Quadrant Converters as we call them.
The ones we calculate are in a somewhat different legue when it comes to power (in the vicinity of 0.5kV and ~150A) but the ideas are the same I would presume.
Anyway, we do not connect the switches in pairs but instead have 4 control pins, one for each transistor, FET, IGBT. That way you could go from TR1,TR4 conducting to (turning off TR4) TR1,D3 conducting and have a path for the current in the top of the bridge. Then turn on T4 and in the next cycle turn off T1 to have a path for the current in the bottom of the bridge, TR4,D2 conducting.
That way you share the load between the two freewheeling diodes D3 and D3 and you don’t have to rely on your voltage source to be able to handle the freewheeling current.