Well, my deranged system is this. I basically only play the Elite Scavenger hunt. I do it because it is one of the few tours where you can end it before the time limit is fully up. The trickiest thing about it is probably just learning your plants and knowing the different bonsai's. But after playing it for a bit, you soon learn that it only uses a small selection of items over and over and so you can learn them and their differences after playing it awhile. Even if you don't know them and have to pick up items to check their description, you can still drop them and find the right items in about half the allotted time.
The time limit for the Elite Scavanger Hunt is 6 minutes but I can finish it in about 3. I've even been able to finish it at 2 minutes or just over if the items are randomly put close by or in the first 3 houses I select. I've finished the tour at over 3 and a half minutes before and still gotten the gold Tortimer medal so you may have 4 minutes to get the Golden Tortimer award before it drops to silver and bronze. I'm not sure exactly since it has been ages since I've got anything less than a gold Tortimer medal. Now, you only get 16 medals for a Gold Tortimer award on the Elite Scavanger but because it can be completed so quickly, I prefer to just take it all the time. I can do 8 tours for 128 medals in about 50 minutes and that's having to go back and board the ship for the tour and get the instructions over and over again.
The other reason I like to take the Scavanger tour is that I can pick up flowers as I'm running around and when I complete the scavenger hunt, I can keep the flowers I've picked up and put them in my basket to take home. After 4 tours, I'll have got 40 flowers filling up my basket and then take them back to my village where I plant them all on the beach. I do that twice for 80 flowers and the 128 medals. The reason is that I want the flowers to go grey and wilt. When they do, I pluck them and this counts towards my weeding badge total. Wilted flowers are treated as weeds. Thus, I find this system works best in order to help me work towards the completion of the gold badge for both those things and is the fastest method to do so. At this point, I only need to do about 14 more of these large scavenger island trips and I'll have got the gold badge for Tortimer Island Tours. Unfortunately, I only learned about the wilted flowers counting towards the weeding total around February so I'll proabably still have to do a few more island tours after I get the gold to get enough flowers shipped in to wilt and die.