OP stated "I export the biped with 'animation' and 'bake animation' ticked and the correct frame segment chosen."

Have you tried to 'export selected' without the bake animation option? Baking the animation could be the reason you are getting unintended animation segments.

In Max the default biped setup is triangle pelvis which parents upper legs to the first spine bone.

To match Unity's avatar structure more accurately - place the biped in figure mode, in the structure roll-out uncheck triangle pelvis. The hierarchy will change as you can see in the schematic view, so the upper legs will now be parented to the pelvis bone.

Biped also links the clavicles to the neck bone by default. To match Unity's avatar structure more accurately - check triangle neck so the clavicle bones link to the top spine bone.

These slight changes in the settings and export process should increase the efficiency of biped matching Unity avatar.