Fun with CDAs..
Right on 'Dumble'...
Well, I start the same way as you...8000 ft=24 miles to run.
Assuming you are on the downwind, start looking at the ILS DME, assuming that there is one..most airports do, for a while the position on the turn is almost like doing a DME arc and it is quite accurate for the CDA.
OK..so far, so good...as soon as 'vector voice' starts to turn us towards the final course...another glance at the DME...do the math...glance at the flight path vector. Your descent rate is similar to what I use..I take the first 2 numbers of the CAS (220K=22..divide those in half=11 put 00 behind it and get 1100 ft. per minute for a 3 degree path. It sounds like a lot of figuring, but I've been doing it for a while and I don't realize it any more...
So then...we start to do the speed reductions, which is why I usually descend slightly below the slope to account for a reduced descent rate somewhere in there...
And, if its all done just right...simultaneous 'green localizer , green g/s' on the FMA.
Of course, if the cockpit load isn't high, this works out really well. But, if we've got wx or like one of our ATC people said, if they need to change the descent rate for planning, things get messed up. But..its fun!