A 4-D Cryptic Crossword

An entry in Fortnightly Topic Challenge #43: Variety Crossword Grids

This puzzle is a cryptic crossword, but with a twist...literally! The grid presented is a 2-dimensional representation of the actual grid, which is embedded on a Klein bottle, and thus has no edges. The top and bottom edges should be identified, and the each column at top rolls into the corresponding column at the bottom, like a cylinder. The left and right edges are also identified, but in reverse order...if you were to print the puzzle out, you would have to twist the right edge, like making a Möbius band, before attaching it. So for example, the eight spaces at left in the fourth row from the top are joined to the right spaces at right in the fourth row from the bottom to make a 16 letter answer.

Because the Klein bottle is non-orientable, answers do not have directions. Rather the clues are numbered from top left, at the first endpoint of each clue...this endpoint may be either the beginning or the end of the answer, and may proceed in either direction (in the case of #15).

Clues

1. $$\left<(100,0,210)\right>$$ contains terminus of ray, and tail (6)
2. Large vessel capsizing un-piloted proa near Tasmania Banks (5)
3. With all the gory details for final destination after careening into nuns? (2,2,8)
4. Alan Rust conflicted over vote for Darwin's term (7,9)
5. Liberal in a tizzy about 2020 event (8)
6. \\$10 blends giving off no fruitiness? (12)
7. Flying, I'm over undersea barrier island (4)
8. Gone after a turn-around (4)
9. Street-urchins start to whine like beggars in East Saint-Louis, abandoned with almost nothing (10)
10. Between sets, to rest the inflamed points, relax tail (12)
11. Stop 'em changing speeds (6)
12. Left with no other (4)
13. In the area over Colorado, getting high, all messed up (5)
14. Sharply focused on article splitting $$xy^2$$, for example, around a leading coefficient (12)
15. Howe song, with the unfinished Beatle arrangement, including back-beat, initially held by Yes, featured first in Month in Syncopation before available to all (3,6,4,2,3,8)

Solver Notes

Extended grid showing three rows of wraparound:

Text grid:

-----------------------------------------------------
|███|   |███|███|███|   |███|   |███|1  |███|   |███|
-----------------------------------------------------
|   |   |   |2  |   |   |   |   |   |   |   |   |   |
-----------------------------------------------------
|███|   |███|   |███|   |███|   |███|   |███|   |███|
-----------------------------------------------------
|   |3  |   |   |   |   |   |4  |███|5  |   |   |   |
-----------------------------------------------------
|███|███|███|   |███|   |███|6  |███|   |███|   |███|
-----------------------------------------------------
|   |7  |███|8  |   |   |   |███|9  |   |   |   |   |
-----------------------------------------------------
|███|   |███|███|███|10 |███|   |███|███|███|   |███|
-----------------------------------------------------
|   |   |   |11 |   |███|12 |   |   |13 |███|14 |   |
-----------------------------------------------------
|███|   |███|   |███|   |███|   |███|   |███|███|███|
-----------------------------------------------------
|   |   |   |   |███|   |   |   |   |   |   |   |   |
-----------------------------------------------------
|███|   |███|   |███|   |███|   |███|   |███|   |███|
-----------------------------------------------------
|   |   |   |   |   |   |   |   |   |   |   |15 |   |
-----------------------------------------------------
|███|   |███|   |███|   |███|   |███|███|███|   |███|
-----------------------------------------------------


Since it's the last day of the FTC fortnight, I felt a little bit rushed, so apologies in advance if the clues seem a little rough.

The solved grid:

AORTA and LOCAL could be entered either way; I've chosen one arbitrarily.

"Zoomed-out" view:

Clue explanations:

I'm not quite sure where the S comes from in clue 10, or what's going on with clue 12 giving LONE.

• Grr...sorry about the flips in 2 and 13, but it also didn't cause any problems, and goes with the non-orientable theme :-) Re: #10, rot13(frgf gb erfg = VAGREF...gur pbzzn jnf n qvfgenpgbe). Re: #12 rot13(lbh tbg zl &yvg vagragvba...jnf ubcvat "ab bgure" = BAR jnf abg gbb zhpu bs n fgergpu). Hope you enjoyed! – Jeremy Dover Nov 28 '20 at 17:18