What was the question that the Referendum answered?
The question was: "Should the United Kingdom remain a member of the European Union or leave the European Union?". It wasn't about "leaving Europe" (as you wrote), it was about leaving the European Union.
There is a document, published by the government before the referendum to meet requirements in the European Union Referendum Act 2015, which tries to make it more precise what leaving European Union could mean: Alternatives to membership: possible models for the United Kingdom outside the European Union. The key part is Chapter 3: The Alternatives. It lists three major alternatives: The Norway model (i.e. remaining in the Single Market), a negotiated bilateral agreement, WTO membership (i.e. no-deal Brexit).
Here is a part about negotiating a deal with the EU:
4.10 It would not be quick or straightforward to establish a new relationship. The models
described in this paper are the result of complex negotiations, conducted over many
years. International trade negotiations are notoriously slow and complicated. The more
comprehensive the agreement, the more drawn-out negotiations tend to be. Negotiating exit
from the EU, a new relationship for the UK with the EU, and then a new set of trade deals with
third countries, would be at the most complicated end of the spectrum. We should expect this
process to take up to a decade or more to complete.
And here is a part about a no-deal Brexit:
It would take up to a decade or more to negotiate a new agreement with the EU and to
replace our existing trade deals with other countries. [...] if we could not reach agreement with the EU on a new arrangement, our trading
arrangements would revert to WTO rules. This would provide the most complete
break with the EU.
From the above, we can assume that by voting "leave" people voted on any of the three above models (the Norway model, bilateral agreement, no-deal Brexit). No-deal Brexit was seen as the last resort, when "a decade or more" of negotiations didn't succeed. So Brexiteers definitely shouldn't be so impatient about the Brexit process after just three years.
Should we have another referendum to ask a question that asks the public explicitly about their preference for customs union, or free trade agreement, or WTO terms, and what their appetite is for disrupted trade? Is it possible to frame such a question, what would such a question look like?
To be consistent with the outcome of the first referendum, the second one could not have "remain" as an option on the ballot, just different deals that the EU can potentially accept, from very soft to very hard, as well as no-deal Brexit as an option. For every deal (or no deal), the voters would have the possibility to mark it as acceptable or not acceptable. This is the way voting was done in the parliament, and I don't see any reason to do it differently in a referendum.
Brexiteers wouldn’t be able to complain that it’s a re-run of the 2016 referendum. It wouldn’t be a referendum asking IF they want Brexit, it would be a referendum about WHAT Brexit they want. I can't see any reasonable argument anyone could have against it.
There are two possible outcomes of such a referendum:
(not likely) There is an option that has got more votes “for” than “against”. It means that we finally have a specific Brexit plan supported by a majority of voters. The Brexit problem has been solved.
(quite likely) No option gets more votes “for” than “against”. Article 50 notification gets cancelled, BUT the public is assured that Brexit is still a possibility. Anyone can propose a new Brexit plan, and if he/she collects enough signatures, a new referendum will be organised. If the referendum succeeds, Article 50 will be invoked again. These assurances can be made into law.
This solution would make Remainers relatively happy: in practice, it would mean Remain for the foreseeable future, as there has been no majority for any specific type of Brexit so far. However, if it turned out that there was a specific deal with a majority support, I think most Remainers would accept the outcome: after three years of the Brexit drama and countless discussions, you cannot really argue that the people didn't know what they wanted for.
It should also satisfy constructive Brexiteers: they would always have a real possibility to have a referendum on a constructive Brexit proposal. Of course, it won't satisfy unconstructive Brexiteers, who don't know what they actually want, but it’s hard to satisfy them anyway.