The Apollo shape also increases the size of the main heat shield-which was half the weight of the command module. Soyuz, in discarding much of the spacecraft's habitable volume, reduces weight thereby. Not saying you're wrong; there are always trade-offs with design.
No, a standard Soyuz's heatshield was less massive because it wasn't designed for lunar-velocity entry, which has twice the heat flux of a LEO entry. Even for Lunar Zond, they had to both use a skip-entry to burn off speed first, and add a much larger heatshield. Plus, to duplicate the 0.3 hypersonic Lift/Drag of Apollo, Zond would have needed even more heatshield mass. So, the Soyuz design
really isn't optimal for mass. Which is, incidentally, why all successful Mars entry vehicles have used an Apollo shape.
The actual advantage of the Soyuz shape is actually monostability: it's only stable in the correct direction for reentry. Apollo, due to its CoG being too far towards the nose, was also (slightly) stable in the nose-first direction. This monostability has saved a few Soyuzes that failed to separate from the SM correctly. On the other hand, Apollo never had a problem with separation, as that's one system that has lots of heritage from satellites.
So, it's not an accident that nearly all the proposed/in-development capsules today (e.g. Orion, Dragon, CST-100, European ACRV, and Russian PPTS) all have conical shapes with 60-70 degrees slopes. Indeed, the original ESAS document describing CEV (which became Orion) has pretty good discussion of the topic:
http://www.nasa.gov/pdf/140636main_ESAS_05.pdf