In December of 2017, I got a 1540 with a 750 reading and 790 math and 20 essay.
I got the exact same subscores in April 2018 with a 19 essay. Should I send both of these tests to showcase my consistency?
No. Why bother? Let them think you only took it once. Send the earlier one, which also happens to have the higher essay score.
I think my high school transcript shows all my tests anyways… And also I was thinking it showcases consistency I guess
Also, my desired school states this on their website: Although we permit Score Choice, we encourage students to submit their entire testing history for both ACT and SAT exams. Why is that
That encourageemt is generally the result of the college’s superscoring tests (using the highest section scores from multiple tests if you submit more than one). In your case, it would make no difference since sending the test with the 20 essay alone accomplishes the submission of your highest section scores. In any event, there is no downside to sending both and you can easily send both in one order per college with SAT and thus you do not pay more for sending both.
If your desired college requests all scores and both scores are on your transcript I would send them both in.