First off, I’m happy to hear that you want to replace your 70-year-old toilet. Older toilets can waste a lot of water and if you install a new high-efficiency toilet you can save thousands of gallons of water per year.
Second, let’s get everyone up to speed on basic toilet rough-in issues. Normally the center of a toilet drain is installed 12 inches away from the back finished wall. This is why most toilet sizes are referred to as 12-inch toilets. Because of installation issues, some toilet drains may be installed a little closer or farther away from the back wall. If that’s the case, you can usually special order “less popular” 10- or 14-inch size toilets.
So, if you can’t fit a 12-inch toilet, your plumber should be able to install a 10-inch toilet to fit your space. To deal with the gap between the toilet and the back wall, I have seen contractors install custom shelving over the toilet tank or even pad out the back wall. So, now you can tell your wife that installing a new toilet won’t be such an “off-the-wall” idea.