Diodorus 23.12-15, trans. Walton. Diodorus's account concurs with Polybius's. While it is more concise on the details of the related battles, it offers a more in-depth explanation of Regulus's peace negotiations with Carthage, shedding extra light on the attitudes of both Regulus and the Carthaginian ambassadors in 23.12. A notable distinction, however, is that in Diodorus's account, the negotiations were instigated by the Carthaginians, rather than Regulus as in Polybius's account. However, this history too may be colored as he later goes to even greater lengths than Polybius to criticize Regulus's behavior in 23.15 (a relatively long section).
Dio Cassius 11.43.20-23 (fragmentary), trans. Cary. Dio is notable for specifying Regulus's reputed demands: to remove themselves from Sicily and Sardinia; to release the Roman captives for free but ransom their own captives; to pay Rome's expenses for the war, plus tribute; to make war or peace only with Rome's prior approval; and to only maintain one warship and yet aid the Romans with 50 triremes whenever the Romans asked. While this list of demands is in character with Regulus's rash behavior overall in the whole situation, modern scholarship indicates that Dio is not necessarily a trustworthy source for historical accuracy.
Eutropius 2.21, trans. Watson. Offers a brief summary of the events. While he seems to be unbiased, he is also unfortunately very brief in his details. He only mentions that Regulus refused to grant peace except under the harshest of conditions, without discussing specifics or motivations.
Orosius 4.8.16 - 4.9.4. (non vidi)
NB: While there are a number of other ancient sources that discuss Regulus himself (such as Cicero, Livy, Horace, Frontinus), they do not seem to be related to this particular issue. Most discuss him as an "example of virtue" on account of the legend involving his patriotism and returning to Carthage to be executed.
Scullard, H.H. "Carthage and Rome," in Cambridge Ancient History (second edition), ed. Walbank et al. Cambridge 1989. In this case, the relevant section is III.c. (pp. 554-557), entitled "The invasion of Africa." Scullard offers an objective view of the negotiations. He mentions the distinctions between Polybius's and Diodorus's reasons for the negotiations. Like Frank, he comments that Dio's list of demands are "scarcely reliable." Scullard is less critical in his analysis, however. He makes no jibes at Regulus, nor does he make an example out of him. He even goes so far as to mention that negotiations would likely have fallen through regardless, since it would be unlikely that Rome and Carthage could agree on what to do with Sicily.
Walbank, F.W. "Polybius, Philinus, and the First Punic War," in The Classical Quarterly 39 1-2 (1945) 1-18. Walbank discusses the contrast between Regulus as criticized by Polybius and Diodorus, and Regulus as exemplified by Horace et al., in his analysis of Polybius's relation to Philinus. Regulus is only mentioned as an example in this case, however, and is not thoroughly discussed in his own right.
NB: The vast majority of the modern scholarship in regards to Regulus, is centered around the later story of him as an "example of virtue" as mentioned above in the ancient sources (particularly in regards to Horace). Included here are a selection of articles which discuss this; however, I will not comment on their applicability to this thesis statement except to state here that they essentially have none. They are listed here mainly as examples of the relative absence of modern scholarship on the topic of Regulus's motivation for and demands at the peace negotiations.
Mix, Erving R. Marcus Atilius Regulus, Exemplum Historicum. Mouton 1970.
Frank, Tenney. "Two Historical Themes in Roman Literature," in Classical Philology 21 no. 4 (1926) 311-316.
Arieti, James. "Horatian Philosophy and the Regulus Ode (Odes 3.5)," in Transactions of the American Philosophical Association 120 (1990) 209-220.
Harrison, S.J. "Philosophical Imagery in Horace, Odes 3.5," in The Classical Quarterly 36 no. 2 (1986) 502-507.