The wording quoted in the question is from an earlier print of the PHB. In later printings, and in the SRD (v5.1, p.188) it reads:

The transformation lasts for the duration, or until the target drops to 0 hit points or dies. If you concentrate on this spell for the full duration, the transformation lasts until it is dispelled

This wording seems to answer the question, that "lasts until it is dispelled" replaces the ending conditions given earlier, but also notes that the effect can be dispelled.

For some reason, this change was never listed in official errata, though the wording did indeed change between printings.

Also, apparently Crawford stated explicitly that this clarification was made on Twitter.

No, you transform back before you can be instantly killed

The rule for instant death says:

Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.

The important part to note is that it only calculates the damage needed to instantly kill you after being reduced to 0 HP.

However, polymorph has a special interaction with dropping to 0 HP:

The transformation lasts for the duration, or until the target drops to 0 hit points or dies.

So when you drop to 0 HP, your form changes. This would happen before the instant death calculation.

The spell then specifically tells us how to deal with damage greater than the HP of the polymorphed form:

If it reverts as a result of dropping to 0 hit points, any excess damage carries over to its normal form. As long as the excess damage doesn't reduce the creature's normal form to 0 hit points, it isn't knocked unconscious.

So, unless the remaining damage brings your original form down to 0 HP and then has enough remaining such that it at least as much as the hit point maximum, you are not instantly killed.

Ruling otherwise is going to be very lethal for PCs and NPCs alike

This ruling makes a lot of sense and ruling otherwise would severely limit the forms that a caster would risk transforming into. For example, most casters would not risk turning into a spider with 1 HP if 2 HP of damage would instantly kill them in that form. The spell is meant to empower the user, not put them at greater risk for death.

But PCs wouldn't be the only ones suffering from a ruling like this. How happy would you be as a DM if your players were able to polymorph enemies into spiders and literally just step on them to instantly kill them?