if I remember, only Calcite can be used on Eternal Pets.
I save my Legend Maps, then use them when it is time for getting the next Legend Map from the Map Feat or Cartographer Feat. although I keep forgetting to check when it is time for the next Feat, I am hoping to get the next Eternal Map, then use the Eternal Map for the next Feat & hopefully end up with a lot of Eternal Maps. best to do this with your Farming Build, since it should have +850% to +1012% Luck.
the Redownload is an exploit that was fixed by the Dev’s in Patch 3.0, by making Players wait 3 hours to play again. remember, if you are waiting 3 hours, you aren’t playing DQ. if you are buying a 1 hour (or 2 or more hours) Monster Boost, and rushing the Enslaver every map, this is lots better than having to wait 3 hours, at least you are getting Loot while working on getting an Eternal Pet. you can do this without the Monster Boost, but then you don’t get Enslavers on every Map. on the other hand, redownloading 8x a day, every day, until you get the perfect Eternal Pet 
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this post shows a Build for Farming Eternal Pets, which increases the chances of any Legend Pet to drop as an Eternal Pet.