I think I know why the method didn't work in this case.
When the number of days was calculated at 152.3, it was assuming that the satellites would be moving and Kerbin was a stationary launch site. This isn't the case. While the satellites moved forward in their orbits, Kerbin was also moving forward in it's orbit. This didn't give the satellites the effective 152.3 day orbit distance from Kerbin before the next launch occurred resulting in the satellites being spaced much much closer than the desired 152.3 days orbital period...
The theory was fully correct however the math needs to include the continuing progression of Kerbin in it's orbital track. Not sure how this would be calculated but hopefully this will allow you to know what to add into the calculations for this type of launch.
As Kerbin is closer to Kerbol than the final satellite orbit, it will have a faster orbital time than the satellites. Therefore, a reverse orbital direction would result in a much shorter time between satellite launches although possibly at a slightly increased DV requirement. Just a thought...
