Well, there are several standard solutions:

1. A significant pause before the final clause.
2. If there is instrumental accompaniment, a different cadence to lead to that final clause.
3. Gesture by song leader.

Et cet. They all work. It's a matter of developing a habitual cue.

The way I understand it, the Agnus Dei must be repeated AT LEAST 3 times, accompanying the Fraction Rite, and only AFTER the host has been broken can "...dona nobis pacem," be said.

It's most common in:

1. Parishes where more bread-like (but still unleavened) bread is used and has to be fractioned. (This is what the rubric is likely envisioning, given that the use of such bread is commended.)

2. Parishes where, contra Redemptionis Sacramentum, a flagon of wine is consecrated and portioned out in chalices after the anaphora. (This is, obviously, not what is envisioned....)

It would seem to me that everyone (assuming they are, as they ought to be!, observant of the celebrant's ritual actions) would know by osmosis.

I have only once come across a parish which sang the Agnus more than three times, and that was because the musical setting used specifically includes a small interlude after the first Agnus, which signifies that it is to be repeated. The choice to sing it more than three times was more motivated by a desire to include that interlude than to extend the Agnus to cover a prolonged Fractioning Rite. In general I would think a congregation would be completely mystified if more than three invocations were sung.

It does sound a lot like how Kyries were sung once-upon-a-time, before the nine-fold (or six-fold) structure was in place. The cantor and choir would just sing Kyrie after Kyrie until the celebrant indicated to bring it to a close, at which point the cantor would intone the final (melodically different) Kyrie.

Change key for the final time
Use "Agnus Dei" to indicate the final time
Use a setting in which the final "Lamb of God" is different than the first two

These would still require the congregation to be "in the know."

I assume that, otherwise, they'd sing "dona nobis pacem," and then just listen to the [in their rightfully bewildered minds] insane choir continue, as some stand and some kneel, whilst looking around to see if others think that it is time to assume that posture...

It is said to "accompany" the fraction -- this is an interpretation, not a rule. It doesn’t have to be micro-managed. Considering that we have been singing the Agnus three times for most of a thousand years, why not just keep doing that?

I shall amend my post.

For how many parishes, places where ideology requires the singing continue until the choir or priest is sick of the music being excepted, does the Fraction take longer than the Agnus Dei, sung 3 times?

There is always the instance, for example, when the singing of the Agnus Dei begins, but the priest is redistributing the hosts in the ciboria so that there is an even amount in each. This can take some time, and in the case of our parish, the priest usually does this before he performs the Fraction. This actually happened at a recent graduation Mass: the organist began the Agnus Dei, but the priest was still reorganizing the ciboria, and the Fraction actually happened after the singing had stopped.

Obviously, you're supposed to use random Christological invocations and then everyone knows it's the last time when you finally get back around to "Lamb of God." Bonus points for inserting subtle progressive agenda theology into your invocation choices.

The use of alternate tropes was never needed to effectively prolong the litany and end with its ultimate line - one can effectively prolong it to cover a prolonged fraction (which does happen if you're not only consecrating single serving hosts) without such tropes. It was not rocket science.

I have one solution that resolves all of this confusion.

I've taken Adam Wood's suggestion and composed a litany that solves this problem:

Lamb of God, you take away the sins of the world, have mercy on us.
Jesus, protector of day laborers, have mercy on us.
Son of God, comfort of LGBT youth, have mercy on us.
Risen Lord, defender of the living wage, have mercy on us.
Christ the King, sustainer of renewable energy, have mercy on us.
Our Savior, provider of universal single-payer health care, have mercy on us.
Lamb of God, you take away the sins of the world, grant us peace.

Feel free to use it at your parish. You're welcome.

At my parish, the Angus Dei is mostly used to signal the end of the sign of peace.