Your swaged bullets will work fine with HB pointed forward. You have the technicalities right in that regard. The lube should be removed. Lay them on a folded towel, in a cake pan, and warm in a kitchen oven till the lube melts and is soaked up by the towel.
Pure lead will do a very precise and smooth job of lapping but casting some of wheel weight metal and air cooling will make the lapping go a lot faster, with optimum lap speed being with hardness of 12 or slightly higher, which means 2 weeks or more aging after the cast.
If one were to purchase swaged soft lead bullets for lapping, best choice would be solid base wadcutters for the calibers available or any of the solid bullets, like RN or SWC.