Long division followed by long multiplication?
That's not division/multiplication, that's a for-loop. When do you perform your corny "proof" operations? After a million nines? A trillion? After infinity nines? Well then you will never have your chance. You can't perform an operation on a value that is never presentable. That is the principle of the matter, and helps explain why everything that sounds hokey about these proofs really is.
Putting an infinite number of 9's, "with a 1 at the end", is nonsense. If the 9's end anywhere, they weren't infinite - so where does your 1 come from?
Your 9's terminate at the initial decimal point. Or did you hope I wouldn't notice? What is that, half-infinite? Is that really the desperation here? Once you see any multiple or offset of infinity appear, you're fucked, and your efforts to rationalize whose infinity is better sounds retarded.
The one day you'd sell your soul for something, souls are a glut.