That's true, but I don't think multiple candidates would have any effect, in the contrived scenario above, on the result of either a by-election or the appointment of a runner-up.

If you modify it so that each candidate is instead a party ticket of two candidates (and assume people vote according to the party ticket), the result in the elections (original and one-seat by-election) would just be 1. BLUE, 2. RED, 3. GREEN, 4. BLUE, 5. RED, 6. GREEN. So the original election would still result in one BLUE, one RED, and the one-seat by-election would still result in two BLUE. And appointing the next runner-up would still be GREEN - I think!

I say 'I think' because I'm guessing they determine the next runner-up just by the final place results, in which case, yes, GREEN gets it. However, if they actually do a re-count of the ballots, except immediately excluding the resigning councillor - RED candidate #1 - then all of that candidates' preferences would flow to RED candidate #2 (again, this assumes that people voted according to the party tickets). The will of the voters - on that day, had RED candidate #1 been struck off the ballot - would be expressed, and the result would be exactly as proportional (in terms of party preference) as it was originally.

I'm guessing they don't do another count, though, because that would take time and money, and the option of appointing the next runner-up seems intended to be the no-spend, no-fuss option.

As an aside, if the process for a vacancy was running another count of the original ballots, it'd mean each ticket would probably want to run at least one more candidate than they expect to win, so that they'd have a backup candidate for preferences to flow to in the new count.

That'd look a little weird if your ticket expects to win all the seats in an electorate, because you'd be running more candidates than seats available. In Ipswich, because there's only two seats per ward, it's not out of the question that one ticket could realistically expect to win all seats (because they'd only need ~66% of the vote). In that situation it'd make sense to run a third candidate - one more than the seats available - in case their #1 or #2 candidate ends up vacating their seat before the next election.

They should probably have a by-election for both seats to be balanced

I think many would argue that kicking out a councillor and making them re-run, through no fault of theirs, is unfair. It forces councillors, who might be independents with limited resources (money, time, volunteers), to spend those resources on a whole extra election, when other councillors don't have to.

It also gives parties an even greater advantage over independents than usual. Parties can, for example, use all their volunteers from the other wards, or even neighboring council areas, to campaign in one single ward, instead of having to spread them across all councils and wards as they must when there is a full local government election on. This is actually an issue with by-elections in general, but it'd be more egregious if you were actually kicking out an independent, who was elected at a general local government election, for no fault of their own.