Peckford didn't really contribute to drafting the charter in its relevant portions here, though he had peripheral involvement in its contours as a premier of a province during the period it was negotiated and as part of the basis for the Kitchen Accord that led to s.33. His major position on the constitutional negotiations as a whole was mostly a losing position. So it's a little like arguing the anti-federalists had unique constitutional insight in the U.S. Especially given that the constitution was shortly relitigated vis-a-vis Meech Lake and Charlottetown and the heirs to Peckford's position... lost again!
After losing election in Newfoundland (thanks partially to betting the province's economic future on hydroponic cucumbers -- a little surprising that didn't work!) he left the province, and he's had no real involvement in politics since except to endorse the far-right political party in the last election and become a professional anti-vaxxer, as you note.
I think the appeal to authority here is odd. Whether Peckford has a legal point on the travel restrictions or not, it's not because he was ostensibly in the room when the finer points of the constitution were hammered out. The whole point of the Court Challenges Program and other measures was because everyone -- the legal profession, the provinces, the federal government, and interest groups -- believed that the charter required extensive jurisprudence to understand.
I doubt Peckford wins as the case works its way through; the dominant policy view on the Charter and the court is basically dialogue theory, that the court exists primarily to work affirmatively with the government and that even when the court strikes government policies it typically does so in a cooperative way. The court is largely deferent to state interests. This deference is built right into s.1, which is why charter rights are subject to s.1.
But even beyond that, the court has already circumscribed s.6(1) rights e.g. in Divito v. Canada (which held that, for example, citizens are not entitled to prison transfers to serve international sentences domestically; both because the state has an s.1 interest in limiting such rights and because s.6(1) isn't that expansive to begin with). The court has never held, e.g., that s.6(1) grants an affirmative right to fly, or an affirmative right to fly without ID, or even an affirmative right to get a passport without following instructions. The alternative argument is some kind of nonsense s.7 argument which would clearly crumble when applying s.1.
I suspect they would decline to rule in Peckford's favour here, they aren't in the business of whole cloth concocting these kinds of affirmative rights. The most likely vote would be 8-1 or 9-0, with maybe Brown dissenting?
Of course Peckford being legally incorrect doesn't mean he has no point from a moral or policy standpoint. Totally reasonable to say "I think Peckford's point is well taken." Just think the bizarre invocation of him as a legal authority doesn't hold up at all.