My experience with a 10 ga. double was that even with 3 or 4 shots out of one barrel did not move the charge in the other barrel enough to detect. This was with 1 1/2 oz. of shot and 110 grains by volume of pyrodex. The thing to remember for over shot wads is that they need to be oversize in relation to the bore diameter. I use 9 ga. wads and they seem to work quite well.
In my double rifle a tight fitting ball / patch arrangemnt works also. I have no experience with conicals in mine as the rate of twist is pretty slow and will not stabilize or regulate with them.
I have not noticed movement in the off barrel with a tight patch and 80 grains of pyrodex- the rifle is a 58 cal.