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I threw together a spreadsheet to find out how much pursuit of Mastery costs… Here you go.

Here is a little explanation:
The costs are cumulative. For example the cost to increase one bird’s class from level 1 to 5 is $3.14. To increase a bird+class to level 10, you’d need 282 upgrades for THAT CLASS at the Mighty Eagle Dojo (half as many if using the 75 LC upgrades).
The totals at the bottom are to upgrade all birds to level 10 via the three different methods. Obviously the cheapest way is to spend 75 LC whenever it presents itself since that upgrades 5 birds and 5 classes by 1000 all at once.
I used the ratio of 85 snoutlings per 500 point snoutling upgrade. And the cost per snoutling is computed from the $44.95 for 1200 Lucky Coins -> Kings Treasure Chest of 17500 snoutlings for 1000 Lucky coins. That is, Lucky Coins cost 3.6 cents each ($0.036), Snoutlings cost 0.21 cents each ($0.0021)
If you’re keeping count, it will cost 10875 Lucky Coins using the 75 LC option and – that’s just for Bird upgrades and doesn’t include buying some of the bird classes! In snoutlings, the total would be 599,250 – but since new single class upgrades only come around every 3 hours, you might get a little bored waiting for the chance to upgrade all classes of all birds via the snoutling route.
Last update to the chart is noted on the chart.