Hi,
Yes, it's possible to avoid these troubles, while dealing with deformed UV space in time, with a help of
Particle Flow. This way you can define the total number of simple "help" surfaces, which can be later used to scatter with Forest Pack in
UV mode.

You'll need to create a
PF Source object and in the
Particle View window adjust the
Event as on attached screenshot. In
Birth operator under
Amount, you can define the total number of "help surfaces" - also I recommend to set the
Emit Start &
Emit Stop to -1. Than you should add a
Position Object operator and assign your object as
Emitter Object. You should mark
Lock On Emitter and
Animated Shape options to follow the deformation. To rotate normals accordingly add the
Speed by Surface operator, select
Control Speed Continuously and mark
Animated Shape, the used
Direction should be set to
Surface Normals. In
Shape operator I recommend to use simple
2D Triangle. The
Rotation operator should use
Speed Space and Y axis should use value of 90. Now the Particle Flow object should be set up properly to follow your animation.

As actually Forest Pack can't use directly the FP Source object as a valid mesh, this needs to be generated with a help of
Mesher object (as shown on
this related post). Create a
Mesher object (
Compound Objects -
Mesher) and pick the previously set up
PF Source object. The Mesher object than should be mapped with
UVW Map modifier with
Face Mapping selected.

Now you can create the
Forest object and use the
Mesher object as a
Surface in
UV mode. If needed, the
Density can be adjusted to get desired number (one) of item(s) for each "help surface". The
Update surface data automatically option needs the be marked to follow the movement.
Attaching simple scene with this workflow used. Hope that helps.
Kind regards,