The same, presumably, applies in America. Parties are willing to sabotage elections altogether there rather than risk making them fairer.
That depends what you mean by "campaign"[0] (or "is", I suppose[1]).
We saw in the 2019 election that individual MPs[2] and even the parties themselves[3] were willing to create electoral alliances for a single issue goal. It is not inconceivable then that an alliance could be formed (perhaps in the aftermath of a hung parliament, or in the run up to a close election) where MPs agreed to introduce a voting system which made the minimum possible change to the existing procedure while also making all future "standing down candidates" alliances unnecessary.
[0] https://www.electoral-reform.org.uk/the-conservatives-just-p...
[1] https://www.electoral-reform.org.uk/latest-news-and-research...
[2] https://www.bbc.com/news/election-2019-50398820
[3] https://www.theguardian.com/politics/2019/nov/07/lib-dems-gr...
Given the failures of campaigns in the UK and Canada to change the voting system, I think that a requirement for proposed systems has to be that the ballot papers (and voter instructions) must be the same as FPTP, and the constituency/district boundaries (and number of representatives) have to stay unaltered too.
That may seem like too stringent a set of requirements, but as you say, a top-two run-off system does satisfy them. Unfortunately, such a system can still be attacked on the basis of cost, since having two election days is roughly twice as expensive as having just one. Not only is there the administrative cost to the government, but the time cost for voters themselves.
The only remaining solution that I have found is Asset Voting, in which votes are cast and tallied just as in FPTP, but then the candidate with the fewest votes gets to reassign their votes to one of the remaining candidates, with this process repeating until a candidate has a majority. This should remove the problems of spoiler candidates and tactical voting.