You sound like a brave man! Trying fool her indoors with maths would never work for me as she would smell a rat immediately! But, if they were all the same colour she would be non the wiser. With regard to your justification figures did you factor in car value depreciation?..Coincidently, I found the spreadsheet that I use to calculate TCO on my cars. In a pathetic attempt to justify my bike(s) to the wife, I added a section that calculates the saving/mile of using the bike, assuming that you keep the car, leaving it at home on the drive. My figures include tyre wear and servicing cost reductions, but by far the biggest element is fuel cost. I don't include car parking charges, as they rarely affect me.
The results are:
30mpg vehicle = 22p/mile saved
40mpg vehicle = 18p/mile saved
50mpg vehicle = 14p/mile saved
So, in my case (30mpg) I had to complete 2700 miles to justify £600 spend.
Of course by the time I built my 4th bike I'd discovered a simpler way - don't tell 'er and hide it my workshop.
I log all my fuel in a phone app and got a new car10 months ago and I have done 4500 miles, spent £680 on fuel and probably lost about £4000 in depreciation..
That would buy a lot of bikes....