Generally, you make your opportunity attack when a creature 10' away from you tries to move farther away from you.
You have quoted most of the relevant text. When it is not your turn, your reach is 10'. The Long-Limbed feature is no longer a factor. So just like any other character, you make the opportunity attack with your polearm when a creature that is 10' away from tries to move further away.
The only exception would be...
If you are making an opportunity attack on your turn, you make the attack when a creature 15' away from you tries to move farther away from you.
The circumstances for this will be rare. If, for example, you are a College of Valor Bard who uses a polearm and you cast Dissonant Whispers on your turn, targeting a creature in melee range with you. The creature fails its save and uses its reaction to run from you. Because it is still your turn, the opportunity attack against the creature is triggered when it tries to leave your 15' reach.
Others have also thought about this very thing, and the rule-text underwent a revision clarifying that all damage dice are to be rerolled
Here is a link to a discussion about this very thing, and below is an excerpt from it:
Overkill was changed to affect all damage dice rolled as of November release, thus making Critical Hits with Overkill hilarious [...]
Without such clarification, the two possible scenarios would be very different
- Unused damage dice do not trigger OVERKILL
In this scenario you would roll 4d6, and choose the two highest, completely ignoring the other two dice. This is somewhat supported as the Critical Hits section says
[...] On a critical hit, all damage dice are rolled twice (including bonus damage) and the highest result from each source of damage is used [...]
Though this does not actually say that the two lower dice cannot be used at all it does say that the two higher dice are used. It may very well be the case that this means they are the only dice used for anything but it may be that they are the only dice used for damage.
- Unused damage dice do trigger OVERKILL
In this scenario you would roll 4d6, and reroll any and all 1's until all four dice read 2-6 (triggering OVERKILL some number of times). Then you would use the two highest dice for your damage roll. This is somewhat supported because OVERKILL occurs "When rolling for damage" and a critical hit's extra dice can certainly be seen as part of the process of "rolling for damage".
The expected amount of gained heat is very different in these scenarios
- In this scenario you would only trigger OVERKILL if 3 or 4 of the dice rolled a 1. Thus 20/1296 crits would add 1 heat and 1/1296 crits would add 2 heat (plus the odds of even further heat being added by OVERKILL). The average heat gained when rolling only 1d6 is .2 and using this we can see that the expected heat gain is the following:
$$.2\left(\frac{20}{1296}\right) + .2\times 2\left(\frac{1}{1296}\right) = .00339506172$$
- In this scenario you would trigger OVERKILL if any of the dice rolled a 1. There are only 625 rolls which will cause no OVERKILL. This is shown in the following calculation, multiplying the odds of rolling no 1's with the total possible number of rolls:
$$\left(\frac{5}{6}\right)^4\times 6^{4} = 625$$
Similarly there are five-hundred cases where exactly one 1 is rolled, one-hundred-fifty in which 2 are rolled, twenty in which 3 are rolled, and one in which 4 are rolled. Just to check, these numbers do add correctly, 625 + 500 + 150 + 20 + 1 = 1296 = 64
This allows us to calculate the expected heat gain as follows:
$$.2\left(\frac{500}{1296}\right) + .2\times 2\left(\frac{150}{1296}\right) + .2\times 3\left(\frac{20}{1296}\right) + .2\times 4\left(\frac{1}{1296}\right) = .1\overline{333}$$
The second scenario has you gaining 39.27 times more heat than the first scenario.
The expected damage is also different
As pointed out by user nick012000 in a comment, the expected damage will not be the same.
In the first scenario you are selecting the two highest dice; however, if either of those are a 1, then you reroll them until they are no longer a one. This gives an average damage of 9.4
In the second scenario, since all 1s are being rerolled, you're effectively rolling dice with sides 2-6 and then selecting the two highest. This gives an average damage of 9.93
You can compare these damage calculations in this AnyDice program made by user Carcer. The difference in damage is 0.53 - nothing major, but certainly not nothing either.
Best Answer
Seeking changes nothing about the nature of the line pattern.
You place the line pattern relative to your character as normal. A Seeking attack hits everything in the pattern, ignoring only those hexes which are somehow physically isolated from your character, not merely behind cover.
Yes, this means the Seeking attack could theoretically have presence outside the targeting pattern.
No, this doesn't mean you suddenly have a spray cone. Seeking attacks generally work with some kind of target acquisition, so regardless of the physical path the attack follows, the targets are still defined in the original pattern.
In this particular case the Balor Nanocomposite effectively uses the original attack's targeting and delivery mechanisms to define the area of operation for the grey goo scenario you're about to unleash, so that what you're creating is a straight 20-hex line bathed in a corrosive nanite swarm that cannot tell friend from foe.
It's alright, if you're into that sort of thing.