Firstly, if you don't know how progressive islands work, refer to this post.

So, I made the best strategies for spending gems if you want to reach a certain node. First, I'll explain how this works:

-For each monster, there are several possible strategies with various amounts of time necessary. I'm also putting some strategies that take longer to complete than the island lasts because, if an island boost happens, the items take 2 times less time to collect, meaning you get twice as many items during those 2 days, which means you effectively get 4 days worth of items in that time, which can also be translated to 2 extra days.

-To find the strategy that suits you, think about how many times will you collect an entire pool of items in the 10 days of the island, and multiply that number with 8 hours to get the amount of total time you want on your strategy. Note that if the number of hours is divisible by 8 on all collections, I put the number of collections as a reference and not the number of hours.

-I'm considering the amount of time required to get items once they are in the pool as 0.

-How the strategy works: For each quest, the strategy tells you the number of gems to spend on that quest. Note that quests which only require 1 breeding item can be completed almost instantly so they aren't included.

It also says after how much time is required to get you to this gem cost if there is no island boost(or if the number of hours is divisible with 8, then the number of collections), which is mainly helpful if you divide it by 8 hours to see how many times you should collect the entire pool of items after you get your first collection. Note that dividing by 8 also works if you're planning for an island boost; just make sure to collect every 4 hours instead of every 8 hours.

If you're going by every hour collection, you might see a remainder when dividing by 8(usually 4, when you get 3 gold and 2 food items without waste); that means that it's optimal to collect an incomplete pool and then gem.

-If you have any other questions, feel free to reply on this thread.

Anyway, here are the strategies(collection of what you can every hour):

Toshiro: /pastebin.com/b352Qbk2

Captain Copperbeard: /pastebin.com/0JngFMmC

M-2 Wyvern: /pastebin.com/gsJfpjPi

And here are for collection every 8 hours:

Toshiro: /pastebin.com/0SYG4tw1

Captain Copperbeard: /pastebin.com/ziFKXJnx

M-2 Wyvern: /pastebin.com/ck1k0WAR

Also, I don't think anyone would want the costs for Sir Francis Rock or Van K. Mark and Mechamancer is really easy to get, but you can request them by replying to this post if you really need them.