Put yourself in a corner and deny yourself things you want...
Ground is a bit of a misnomer, you are actually eliminating the potential voltage between yourself and the system you are building. So, in such a case, you will ground yourself to the chassis. Paint is rarely an issue. You can always find an area that won't be seen and remove some of the paint.
Really grounding straps are not strictly necessary. As long as you make sure to touch large metal components constantly you should be fine.
1) The outside of an anti-static bag is rarely anti-static, so touch the inside of the bag during removal
2) When you remove a component, touch the chassis before touching the component to any part of the chassis
3) Any time you walk away, touch the chassis before handling any components inside the chassis
If you pay attention, you will notice this pretty much happens during construction.