I am thinking you have the seating die down too far. Back it way off so that it doesn't do any crimp at all. Also, try belling the case mouth a little more so starting the bullets is easier. I use the factory crimp die for pistol ammo as the last step.
I may be wrong, but .002" on cast is ok. Not sure tho.
I agree with Heavies. It appears that your crimp is too heavy. The extra effort to seat the bullet is what is deforming the sides of the bullet. Also, the shape of your seater doesn't match the shape of your bullet.
My suggestion is to make a few dummy rounds.
1. size and bell a few cases with no powder or primers.
2. screw out the sizing die just until it doesn't touch the case.
3. put a bullet in a case, keep running it into the die and screwing in the seater until the bullet is just a hair above where you want it to be.
4. screw out the seating part of the die.
5. run the case up into the sizing die and screw down the sizing die until you can just feel it touch the case.
6. with the case in that position, screw in the seater die again until it touches the bullet.
7. turn in the die assembly in at maybe 1/4 turn increments and see how the bullet/crimp looks.
The shape of your seater for the .270 also doesn't match the shape of your bullet, as Heavies noted. I have had problems with Lee dies before, and have gone to RCBS, Hornady or even Redding for higher quality. Some of the die makers make a separate seating die, which I have used.
Not to bash Lee dies. I use their carbide dies for pistol calibers.
If you have other Lee pistol dies, look at the seaters and see if there is one with a flatter seater. They may interchange.