Where should "never" go in "Harris Should Have Never Run for President"

This seems to be an American English vs British English issue. Here are the results of searching for these phrases in the Corpus of Contemporary American English (COCA, 560 million words) and the British National Corpus (BNC, 100 million words). The percentages are the out of the total number of hits for all three phrasings in that corpus, i.e. 193/(193+840+480) × 100 = 13%.

                                          COCA                  BNC
should have never         193  (13%)           1   (0.4%)
should never have         840 (56%)        237 (97%)
never should have         480 (32%)          6    (2%)

Clearly, should have never is rarer than the alternatives in both COCA and BNC, but in the BNC it is much rarer. In COCA, it is 4.4 times and 2.5 times rarer, while in the BNC it is 237 and 6 times rarer.

Interestingly, never should have is also quite rare in the BNC, 40 times rarer than should never have.

For what it's worth, here are some examples of should have never in the published literature:

I should have never valued the Blackcoats' useless revolution over Benjy's life. (source)
I should have never moved here Frances. (source)
I should have never listened to you! (source)
He should have never put her in the middle of this situation. (source)
She was a halfbreed, the spawn of a marriage that should have never taken place. (source)
If we are so-called Americans, things should have never been this way. (source)
I should have never, ever let her crawl under my skin as she has. (source)
The evening was nice, but should have never taken precedent over the academics. (source)

For many, many more examples, see here.