Here is my conclusion (in short, no solution):
1- (Edit: unfortunately this point is not correct, you wont get the updates unless you download directly from the store.) The only issue is delivering the first APK to the testers, as they wont be able to download the application from the Play Store, however, downloading updates from the Play Store is doable and okay, (delivered APK must be signed with same key as Play Store APK).
2- If the application is never publicly released yet, testers must have some sort of a direct link to the application on the Play Store, as searching for it will never show up (even with package name: com.example.application). But after having the first APK, you can just look through the 'My Apps" section in the Play Store and find it.
3- Google sucks for not making this easier, especially given the triviality of the concept and the need for it.
Thanks everyone for your suggestions. But considering none of them were the answer, because there is no answer, I had to sum up my findings here.
Cheers.
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