Forced/unlikely answers are usually true

Question

I heard in a shiur that the Chasam Sofer says something like רוב דחוקים אמת, most unlikely answers to a kasha are true. It's not clear to me if this means it is the correct answer or simply there many answers and these "bad" ones are included (similar to אלו ואלא)

1. Where does he write this?
2. Does anyone else express this idea?
3. Does anyone explicitly argue on this idea?

Answer 1

The Mishneh Halakhot (Vol. II: 24) explains:

יותר טוב לישב דברי הראשונים ז"ל אפילו בדוחק גדול מלאמר דנעלמה מהם גמרא מפורשת בכמה מקומות בש"ס ועיין בח"ס ריש כתובות שכתב רוב מהתרוצים הדחוקים אמתיים הם וז"פ

That is, it is better to give a forced explanation of the Rishonim than to suggest that they forgot explicit passages in the Talmud. Thus, the intent is clearly that when forced to give an answer (since the alternative is even less likely; that they forgot explicit passages) the answer is usually correct. This would have nothing to do with אלו ואלו.

As his source he cites Hattam Sofer to the beginning of Ketubot, but I did not see it there.

The Mishneh Halakhot also quotes this in (III:2).

Answer 2

1. This was written by Chassam Sofer in a responsum to R. Moshe Gluga (dayan of Zelem/Deutschkreutz) relating to a prior correspondence they had regarding a question posed by the latter. R. Sofer dismissed the question , one reason being that it would it would call into question the particular opinions of Tosafos R. Isaiah de Trani (Ria"z). In the ensuing resp., CS tells RSG:

ואם אולי יש את נפשו תירוץ אחר... יודיעני ואודה לו ובלבד שתירוצו יהי' גם כן סברה ואפילו מדוחק, כי הדוחקים רובם אמתיים, אמנם השכליים וההמצאות רובם שקר, והם המכסים פני האמת וגורמים לבעליהם להחזיק בשקר בתורת ה', כי רע בעיניהם להודות על האמת ולעזוב החריפות שלהם

My attempt at a loose trasn.:

...If you have an answer to reconcile the Tosafos and Ria"z... let me know it and I'll thank you, even if strained as long it is rational because most strained answers are true. However, savvy and novel ones are mostly false; they only obfuscate the truth and give way for the respondents to perpetuate falsity in Toarh, because it is hard for them to admit to truth and withdraw from their harifus..." (Chassam Sofer, Kovetz Tshuvos EH no. 82)

2. I don't know an explicit source expressing exactly this but I don't think this is such a grand observation. In context, CS was illustrating how much pilpul and harifus that was (is) common is fallacious whereas sensible, rational answers, even if they don't exactly fit, are more accurate and plausible answers. This sentiment was echoed by many rabbis, much before CS too.
3. I do not know of anyone disagreeing with this sentiment.

Returning to your opening query, IMO, CS did not mean that such an answer would be the correct answer, rather, it is more likely [than the second class].