That which the Magen Avraham writes in Siman 607 in the name of the Shelah Hakodosh to say סליחה לעונות ומחילה לפשעים is certainly a copyist error, because in the sefer שני לוחות הברית itself he writes the opposite, and it is impossible to suggest that there it is a copyist error since he explains the reasoning behind the wording.
However, if not for the words of the Shelah it seems to me that we should say סליחה לעונות ומחילה לפשעים, because we should always use the language of Torah whenever we can, and we never find the word מחילה anywhere in the Tanach, but we do find that כפרה us used in connection with חטא, as it says אכפרה בעד חטאתכם and וכפר עליו הכהן מחטאתו, and in many other places in the Torah, but we never find in the Torah כפרה used with עון or פשע. It’s true that in the Prophets and the Writings we find כפרה used with עון many times, for example, בחסד ואמת יכופר עון and בזאת יכופר עון יעקב and והוא רחום יכפר עון, and so too we find כפרה used with פשע once in Tehillim - פשעינו אתה תכפרם, nevertheless, in the Torah we only find it used in connection with חטא.
And סליחה we find in the Torah used with the word עון, as it says, סלח נא לעון העם הזה and וסלחת לעוננו and we also find סליחה used with חטא many times, for example, מחטאתו ונסלח לו, but with all of them כפרה us written beforehand. But we never find either כפרה or סליחה used with פשע. And even in the Prophets and the Writings we do not find סליחה used with פשע, except one time in Megillas Eichah - נחנו פשענו ומרינו, אתה לא סלחת, but there it is used negatively.
Therefore, we should use the language of the Torah - כפרה with חטא, and סליחה with עון. But we never find that סליחה is used with פשע, and therefore we should use the word מחילה in connection with פשע since we cannot say it in the way that it is written in the Torah.
And regarding what the Shelah wrote that the word סלח signifies lengthiness, this is what I have to say: When I searched for some support for the word מחילה in לשון הקדש, I did not find the root of this word - it is not from the root חול, nor from the root חלה. Nor can it be compared to the root אחל which is an expression of requesting. The only support I found is that it might be from the root יחול which connotes "looking forward to", like יחל ישראל. If so, unlike what the Shelah says, it is the word מחילה which signifies lengthiness, but the word סלח is translated by Onkelos as שבוק - abandon.
Thus, it would seem to me that we should say סליחה לעונות ומחילה לפשעים, but since the Shelah testifies in the name of the Rema to say מחילה לעונות וסליחה לפשעים, far be it from me to argue with him. Also, in the Piyut which we say after each סליחה the text is מחילה לחטאים וסליחה לפושעים, which implies that מחילה us more than סליחה, like the Shelah said. And indeed, in the gemara Yerushalmi at the end of mesechta Yoma the text is כפרה לפשעים, מחילה לעונות, סליחה לחטאים.