I like this strategy very much, and have found it useful. I have implemented it in my own solver, along with finned x-wing and finned jellyfish - no need to go to larger fish, because the existence of a larger fish (finned or not) requires the existence of a conjugate fish which is of jellyfish size or smaller.

On the "Aligned Pair Exclusion" page, I have described a strategy I have implemented in my solver, which I call "dynamic locked sets" - it is a generalisation of the idea of an ALS in an alternating inference chain. Most useful in a forcing net, but it could come up in an AIC as well. I have similarly implemented, within my "forcing net" algorithm, dynamic groups, dynamic finless fish, and dynamic finned fish.

Here are the statistics on how many puzzles in my small database of 245 can be solved using my forcing net software, with its various dynamic options. Every combination is shown, except that there is no easy way to include finned fish without also including unfinned fish.

Basic (no "dynamic" options) - 165
With dynamic groups only - 168
With dynamic locked sets only - 169
With dynamic finless fish only - 167
With dynamic finless fish and dynamic finned fish only - 195
With dynamic groups and dynamic locked sets only - 173
With dynamic groups and dynamic finless fish only - 169
With dynamic groups, dynamic finless fish, and dynamic finned fish only - 203
With dynamic locked sets and dynamic finless fish only - 172
With dynamic locked sets, dynamic finless fish, and dynamic finned fish only - 206
With dynamic groups, dynamic locked sets, and dynamic finless fish only - 173
With dynamic groups, dynamic locked sets, dynamic finless fish, and dynamic finned fish - 209

The final 209 number includes a good number of the "unsolveables", although this technique definitely remains stumped by some other unsolveables.

Granted, 245 is not a huge sample, but based on the results above, I feel like there could be a lot of mileage to be had by incorporating the concept of an "almost (finned) fish" into the AIC algorithm, or its generalisation, a "dynamic (finned) fish" (either in an AIC, or in a general forcing net).

Something to consider :)

I used my own solver to find some examples on finned/sashimi sudoku and found something interesting.

While solving puzzle
080040070000005800040700020063500002200000005800002760010007030009300000050080010

after some singles and finned X-Wing, puzzle gets into this state:

+---------------+------------------+-----------------+
| 1569 8 2 | 169 4 1369 | 13569 7 169 |
| 169 3 7 | 16 2 5 | 8 49 1469 |
| 1569 4 16 | 7 1369 8 | 1356 2 136 |
+---------------+------------------+-----------------+
| 14 6 3 | 5 7 149 | 149 8 2 |
| 2 7 14 | 8 1369 13469 | 1349 49 5 |
| 8 9 5 | 14 13 2 | 7 6 134 |
+---------------+------------------+-----------------+
| 46 1 8 | 2469 5 7 | 2469 3 469 |
| 7 2 9 | 3 16 146 | 46 5 8 |
| 3 5 46 | 2469 8 469 | 2469 1 7 |
+---------------+------------------+-----------------+

My solver printed
"Finned Swordfish
On candidate 4. A fish goes from Column 1, 8, and 9 to Row B, D, and G. On Box 6, the fish has two fins E8 and F9. Therefore...
4 taken off from Cell D7."
(Actually this is a sashimi, but it was meaningless to tell sashimi apart from finned one.)

A sashimi swordfish with two non-aligned fins. I used your solver to see how it solves the puzzle, (turned off GXC and ER) but seems like the finned swordfish algorithm does not find this case.

I'm trying to implement finned/sashimi swordfish in my own solver and using your solver to verify results.
While solving puzzle 7.9.........4..2.7.2....3...72......3...17.6.9..2...345347..1.929.........1......

After some other steps, puzzle gets into this state:

+--------------+-----------------------+------------------+
| 7   568  9   | 13568  23568   123568 | 4568  1458  1568 |
| 1   568  3   | 4      5689    5689   | 2     589   7    |
| 4   2    68  | 15689  7       15689  | 3     1589  1568 |
+--------------+-----------------------+------------------+
| 68  7    2   | 35689  345689  345689 | 589   158   158  |
| 3   4    58  | 589    1       7      | 589   6     2    |
| 9   1    568 | 2      568     568    | 7     3     4    |
+--------------+-----------------------+------------------+
| 5   3    4   | 7      68      68     | 1     2     9    |
| 2   9    7   | 135    345     1345   | 4568  458   3568 |
| 68  68   1   | 359    23459   23459  | 45    7     35   |
+--------------+-----------------------+------------------+

There is a sashimi swordfish in rows 2, 6, 7 and columns 3, 5, 6 with fin in r2c2 which eliminates 6 from r3c3.

Am I missing something or just found space for improvement of your solver? Which is brilliant anyway.

In order not to miss out on possible finned swordfish scenarios I would just like to confirm that I do understand the exact definition of this configuration correctly. Does the "fin" have to be the a second or third candidate in one of the defining columns (or rows) of the swordfish, or can it actually be a fourth candidate in a defining column (or row)?

The explanation of example 2 is flawed or the description of the rule is wrong.

Applying the same logic as in the Finned Sashimi Example 1 to Example 2, I find an 'imperfect' 2-1-2 SwordFish in columns 1, 6 and 7.
Accordingly, A6 in Example 2 has the same role than H2 in Example 1; a cell of the SwordFish that does not contain the candidate.
Thinking in columns the 'fin' would be B6; restricting elimination to the box of the SwordFish, A4 and A5 could be deleted.

The example argues the other way round: A4 and A5 being a 'double fin' and B6 to be deleted!

Where is the fault?