What is the past tense of 'to be' on a 747? Will we need new language constructs to accommodate time-travel usage?

I think there's two questions here: when time traveling, what are the limits of what the English language can express, and how will people avoid ambiguity.

The latter has an infinite number of answers. English has two proper tenses and some auxiliary verbs, Chinese has zero, and other languages may have many more. Perhaps frequent users of the 747 will develop a system of prefixes, or extra verbs, or new tenses. All is possible, and it is hard to judge which system will be more likely to arise. I expect the first community of time travelers to have say in it.

But the first question can be answered. English is, like the human experience, predicated on a flow of time that is both linear and traveling in the same direction for everybody. As said in the comments, one way of dealing with one person's temporal hijinks is to treat the personal experience of time as the baseline for tenses, rather than the universal experience (which is no longer universal).

So, using that system, "I will go hiking yesterday" is perfectly non-confusing: in the future, you will go to the past, and go hiking. Conversely, "I went hiking tomorrow" means that in the past, you went to this tomorrow. "Tomorrow" and similar words are never assumed to calculate from any time frame than the moment of speaking, so that posed potential ambiguity feels unconvincing.

It gets more complex when not talking about one's own flow of time. "You went hiking tomorrow". "Went" from whose perspective? Either the speaker has been in tomorrow, saw the listener hiking, went back to today, and told them that they saw them hiking - an act which the listener may or may not have already carried out. But if "went" refers to the listener's perspective, then unambiguously the listener has already been hiking tomorrow and is now back in the today.

It grows much more doozy when it's the collective. "We went hiking tomorrow". It could be in the past for one person or both. Is this something the listener is still to plan for?

Now obviously there's many ways to solve this. A clever multi-dimensional calendar app can put appointments at various temporal distances from fixed dates - though I do not envy the programmer in charge of making that system handle daylight saving time. And there's also linguistic solutions in various forms. Talk at a higher pitch when discussing time from the listener's perspective, or prefix all references to time with the name of the person experiencing it. Or add more tenses. Go wild!

But in conclusion, the biggest issue that I think time travel appropriate language will need to solve is accounting for different people's temporal experiences and clarifying which experience is meant when discussing time in any non casual sentence.