This is the type of case that Rav Eliashiv was referring to in his published teshuva (3:140) and it is the type of case that most poskim would agree that it is appropriate to convert the non-Jewish spouse. The insistence of having conventions and pursuing people who knowingly sinned by intermarriage is not validated by this approach. The attempt of Roni and R' Tropper to insist that leniencies such as this allow them to hold conventions to persuade intermarried couples to convert requires clearly stated teshuvos to that effect from Gedolim. Even their posek Rav Reuven Feinstein has not issued a heter for this nor has he stated publicly that it is permitted.As far as I can ascertain - Rav Reuven Feinstein does not disagree with Rav Sternbuch on this issue.
סימן ה:שבב
הערה נענין נישואין לבעלת תשובה
באו לפנינו מקרים של בני תורה שהתחתנו עם בעלות תשובה, ואח"כ נתברר שאם הכלה היא גיורת שנתגיירה ולא שמרה מצוות מעולם, ואומדנא דמוכח שלא נתכוונה בשעת גירותה לשמור מצוות, והפוסקים כתבו שלא חלה הגירות והיא עודנה בגויותה, וכן בתה, אף שהיא בעלת תשובה וצדקנית ונשואה לבן תורה, מ"מ מדין תורתה"ק היא גויה ובעלה חייב לפרוש ממנה, והטבלנו אותה בצינעא בפני בית דין לשם גירות, ובעלה קידשה ונשאה עוד פעם בפני עדים כדין. זה הוא אם אמה של הכלה נתגיירה ולא שמרה מצוות מעולם, אבל אם אמה של הכלה גופא החלה אח"כ לשמור מצוות, אין לי הכרעה, ומ"מ צריך לחומרא להטבילה...
Rav Sternbuch (Teshuvos V'Hanhagos 5:322): Concerning a marriage to a baalas teshuva. We have cases coming before us of a ben Torah marrying a baalas teshuva and then afterwards it is discovered that the bride's mother was a giyorus who never observed mitzvos. It is reasonable to assume that the mother had no intention of observing mitzvos at the time she converted. The Poskim says that therefore the mother was never a convert and thus she is still a non-Jew and obviously so is her daughter the bride. This is so even if the bride is a genuine baalas teshuva and truly righteous and she has shown her sincerity by marrying a ben Torah. Nevertheless according to the law of the Torah she is a non-Jew and her husband must separate from her. However she is to be immersed in the mikva secretly before a beis din for the sake of conversion. Her husband needs to marry her a second time in the presence of kosher witnesses. This is if the bride's mother converted and never observed mitzvos. However if her mother eventually did come to observe mitzvos - it is not clear whether the daughter is Jewish but she should l'chumra be converted....