I'm a bit anal about engine cooling, so I use a rule of thumb of 5 miles per 1000' - it make my poor mental maths a bit easier too.
As I'm normally interested in getting to the aerodrome rather than a bimble of a certain duration, at the descent point I will just stick the nose down and hold cruise power and take the increased airspeed. After a minute or more, if needed, I'll start to pull MP as required in steps of 1 or 2" to hopefully end up at circuit height with the speed bleeding off about 3-5nm before the aerodrome.
But presented with the original problem in the air, I would probably go:
15nm away less 3 is 12, less another 1 whilst I work this out (and while flying the plane and talking to ATC) is 11, which is close enough (for government work) to 10nm
10nm at 110kts is near enough 2nm a minute, so 5 mins
3000' to 1000' is 2000', less 400' for QFE is 1600'
1600 divided by 5mins is a bit over 300fpm
Yes, the errors can accumulate, but I wouldn't try to use any VSI that I have come across in a GA aircraft to 100fpm resolution, so working things out to the nearest 50fpm or finer is a waste of time IMHO