If the problem is the time it takes to "take 20", that can't really be solved with a rule. The effect of time passing IG is completely dependent on each situation.
My problem with taking 20 is not the time, it's that it has removed all random chance from the outcome. They either always find the item/trap/door, or they never find it. To add this random element back in, whenever the PC can "take 20", the player instead makes a normal skill check and then adds 10 to the result. That on average equates to about the same as "taking 20" but it allows for a more random distribution of the outcome.
My problem with taking 20 is not the time, it's that it has removed all random chance from the outcome. They either always find the item/trap/door, or they never find it. To add this random element back in, whenever the PC can "take 20", the player instead makes a normal skill check and then adds 10 to the result. That on average equates to about the same as "taking 20" but it allows for a more random distribution of the outcome.