I'm no Expert, that's for sure. But, following up on what the other guys have said (and learning along the way):
1. The Loop Cut and Slide (Ctrl+R) I do not think will work with the geometry in the .stl file;
2. As mentioned, If you had the extra horizontal vertex loops you mentioned that you could add, you could select an entire loop, turn on Proportional Editing mode (a radio button in the viewport header or available from the Mesh menu) adjust the Falloff and the size of the effect (middle mouse button) and then scale the edge loop;
3. Add more mesh density, either by the extra horizontal vertex loops or by using the SubSurf Modifier (although I think this latter Modifier will change your whole mesh wish I'm guessing you don't want). Then set up a Lattice Object and use the Lattice Modifier. I have never used this (didn't even know about it until this thread) but just watched this
video and think it looks exactly what you need. I recommend the tutorials by this guy, Neal Hirsig, to everyone.
In any case, I'm pretty sure you'll need to add more mesh to do what you want to do in Blender.
Good Luck