Fluid dynamics is certainly not my thing and with all sorts of issues at play like non-symmetrical surfaces, rotation perpendicular to gravity, changing viscosity of the epoxy, etc. etc. this is probably a complicated issue. To a first approximation, I would guess that a fluid enough filler material of enough volume would flow to the largest diameter and form a uniformly round inner diameter, heavily coating thin spots and thinly coating thicker spots. At any given height along the rotation axis I would expect a constant radius to the inner surface, but I would expect the radius of that surface to change as the height along the axis changed but not necessarily follow the contour of the outside of the top. By that I mean I expect the final wall thickness to be uniform around the top (provided the outside was symmetrical) where adequate filler was supplied but I do not expect the final wall thickness to be uniform along the rotational axis.
I found a photo sequence of a Hydro Gyro toy (a fluid filled top/gyroscope launched by a ripcord) used horizontally in a gravitational field. Without rotation the liquid rests in the lower half, with some rotation the liquid is more uniformly distributed but not perfectly, with high speed the liquid is uniformly out to the largest perimeter of the allowed volume. Although this volume is symmetrical, I would expect the same uniformity of the fluid’s inner diameter for a non-uniform shell.
Does this mean the top will be balanced? Not necessarily because the non-uniformity of the wall thickness is over all the body of the top and to get the uniform filler surface everywhere, one would have to basically fill the entire volume. Of course there may be some middle ground because the tip section is very close to the rotational axis and plays a more minor role.
Perhaps a different approach would be to again use a filler of similar density to the HDPE but with a very high viscosity and short work life and apply it like butter on toast or frosting on a cake while the top is spinning. This would be applying material to a fixed diameter at each height along the axis of rotation thus creating the symmetrically thick wall.
I think putty is still looking pretty good.