As promised, I refined my approach to determining the location of 9 Maidman Street. Instead of relying on the orientation of the maps, I used a differential approach which made the map orientation irrelevevant. I also put the origin of my vector further away from 9 Maidman, and used a longer reference-distance to determine the distance-ratio, in order to reduce the effects of measurement errors. The result is a point about 40 feet from my first attempt to pinpoint the coordinates of the former 9 Maidman Street (after finding a map which showed the locations of the buildings). I also repeated this process using a longer reference-distance, and got a point about 7 feet to the east of the 1st attempt using the differential technique. I then repeated it using Google Earth and got a result which is approximately in the middle of the previous three attempts. All of these four attempts are clustered around the "H" which can be seen to the SW of the intersection of Mile End and Burdett in Google's satellite photo of the area. A "best fit" line drawn through them had an angle of about 75/15, meaning that all of them would have essentially the same bearing relative to St. Paul's Cathedral. But in case anyone is interested in the coordinates:
Single-ended approach: 51.524422°, -0.035126°
1st attempt, using Google Maps: 51.524399°, -0.035309°
2nd attempt, using Google Maps: 51.524392°, -0.035276°
3rd attempt, using Google Earth: 51.524415°, -0.035222°
When I zoom out in order to get the big picture, all four of these points become indistinguishable, although my original location for 19 Maidman, on the other side of Burdett, is clearly distinguishable.