After posting this, the author wrote to let me know that he disagreed with my title for his post, as will become apparent in the following copy of his letters. I highly recommend that if anyone is doing work on Mitzvos Tzrichos Kavana that he read these letters and see the Mar'ei Mekomos.
The connection you made in the title is interesting. I think it's incorrect but I have to think why. Few random initial objections are:
Probably you agree that the need for Tshuva in Y"K has nothing to do with מצוות צריכות כוונה. (Kapara of Y"K is not a Mitzvah, so why would it need כוונה anyway; moreover כוונה everywhere else is just to be יוצא; this is not the same as Tshuva). Thus I don't accept the equation between אינו מתכוון and אינו שב.
The link you made to מצוות צריכות כוונה is probably only as far as כוונה הפכית may nullify a Mitzvah, which could be the same idea as מבעט. Still, I think this is not the same (if only for the fact כוונה הפכית is Machlokes Rishonim, while מבעט is Machlokes in Gmara and maybe Tanaim), but I have to figure out better why is that so.
One difference coming to mind is the question of כוונה הפכית במצוות שהן מכשירין.
Even if we consider מבעט as כוונה הפכית, one must agree that what we talk about here has nothing to do with לצאת ידי חובת מצווה but rather with attaining כפרה, i.e. it's a מכשיר.
This is discussed in length in various Achronim, some say it's the same as regular Mitzvos, e.g. Maharshal says Shchita with כוונה הפכית is invalid. However, some disagree, e.g. Radbaz. Lengthy discussions see, e.g. Melo HaRo'im http://www.hebrewbooks.org/pdfpager.aspx?req=33736&st=&pgnum=236 Oneg Yom Tov Y"D #57 http://www.hebrewbooks.org/pdfpager.aspx?req=1104&st=&pgnum=175 and Sdei-Chemed http://www.hebrewbooks.org/pdfpager.aspx?req=14145&st=&pgnum=131 .
Moreover, even if we accept the former and agree that כוונה הפכית works even for מכשירין, one may argue that this only works as far as the הכשר is achieved through a מצוה (like Shchita, Halitza or Tvila), and depends to some extent on human action. Here we deal with כפרה that is ממילא and has nothing to do to anything the person does, why would his כונה matter at all?
Finally, Rashi in Krisus there explains that the premise that אין מכפרין אלא לשבין follows from לרצונו. That is, there is a special דין רצון in Kodshim, which then can be argued to cover not only רצון for the הקרבה but also for כפרה.
Based on the above, the Machlokes re: מבעט can be worked out either way. Whatever we hold regarding כוונה הפכית, one can still say this is not relevant for מכשיר דאתי ממילא and therefore the issue there has to do with לרצונו.
However, it is true that many Achronim explain that Rabenu Shmuel who says that כוונה הפכית works even if מצוות צריכות כוונה holds that the Mitzvah is complete even without כוונה but nevertheless one cannot be accredited against his will (this is the common Teiruz to the Turey-Even, attributed to R. Shlomo Heyman, found also in Kovetz Shiurim, Hazon-Ish, etc). This logic could be extended to מבעט too, but not necessarily so.
While being focused on trying to prove myself right, I didn't realize what most bothered me with the title -
I now think the main problem I have with it is that it distracts the reader from (what I consider) the main
novelty here - that even according to רבנן דרבי Y"K is still מכפר with no תשובה, contrary to the common
understanding. What do you think?
Kovetz Shiurim 33.
Chazon Ish: http://www.hebrewbooks.org/pdfpager.aspx?req=14336&st=&pgnum=90
R. Shlomo Heyman: http://www.hebrewbooks.org/pdfpager.aspx?req=3281&st=&pgnum=8
They each have their own version and style, but basically say the same.
I'm quite sure there are more, but I don't remember the names so I can't look them up.
It's interesting how for generations the common wisdom was to explain in one way (here, something
along the lines of סתמא לשמה), then all of the sudden many come up with another idea.
I've seen many other examples of this. Either these are manifestains of zeitgeist, or else
this idea was part of the ישיבישע רייד and was somehow adopted by many (but Chazon Ish ???)
BTW, see Chazon Ish comment at the end there - how does this work for מבעט?
More to the point, while looking around I found this (#28): http://www.hebrewbooks.org/pdfpager.aspx?req=1501&st=&pgnum=57
So, can we agree on the bottom line: the link מבעט-מכוון שלא לצאת is possible but not necessary ?
[Your ראיה from משתלח is very nice indeed! (Note: I had mentioned that the Rambam in the beginning of Hilchos Teshuva says that a מבעט in Sa'ir Hamishtalei'ach is miskaper on 'kalos' but not on 'chamuros.')
1. what about מבעט in other קרבנות צבור I don't know where to look.
2. could that be Machlokes Rabbi and Rabanan - whether Y"K as מכפר is individual
or communal? IIRC, there is a long discussion on כפרת היחיד וכפרת הציבור in R. Soloveichik's על התשובה]
(Note: my son spoke on Yomtov and used a great many of these mar'ei mekomos; and he made an interesting point. Rashi in Sukkah 26a, which is the basis of the Magen Avraham/Mishna Berura in 38, says that Osek be'Mitzvah is only pattur min hamitzvah when the primary motivation for his ma'aseh mitzvah is to be mekayeim the mitzvah. If his main motivation is to make money, then he has no petur of osek be'mitzvah. It is obvious that this extreme limitation on the definition of oseik bemitzvah would not apply to the definition of "kavana" as needed to satisfy the Mechaber's opinion (see Sdei Chemed) that lehalacha Mitzvos tzrichos kavana.