Great method! However, I was finding that it was fairly straightforward doing it in the comfort of my own home but when out and about in loud and distracting public places there was an element of performance pressure that sometimes messed up the mental arithmetic or slowed me down. To counter this I now divide by seven for each element of the date as it is given i.e 24th = 3, 17 = 3, 11 = 4, 21 = 0 etc and keep a tab of the remainder by putting my thumb against one of my fingers 1= thumb on index, 2 = thumb on middle, 3 = thumb on ring, 4 = thumb on pinky, 5 = thumb on none of the fingers and 6 = closed fist (or any system that is easy for you to remember). That way I am keeping tabs on only one aspect of the date at a time and have a tactile reference point that I can refer back to and is easy to maintain while talking or figuring out the next number to add.
So the 16th September 1976 would be calculated as follows:
16th: remainder 2 (thumb on middle finger)
September: + 4 = 6 (fist)
70s: 6 + 4 = 10 - remainder 3 (thumb on ring)
76: + 6 = 9 - remainder 2 (thumb on middle)
Add 2 for leap year - (thumb on pinky)
Pinky = 4 (Thursday).

Has worked well for me and certainly takes the pressure off as you only gave to keep tabs of small numbers.