Which of these interpretations of the definition of a cone's area of effect is the correct one to base my template design and construction on?

Answer: Option 1

You say:

The problem is that the rules for the shape of a cone AoE aren't very precise, and when you start looking at them closely, there are a bunch of inconsistencies.

and

There are three incompatible interpretations of the maximum length of a cone

I disagree. It is clear what precise shape they describe, and it is the simplest way to describe and use a cone area of effect in this game, particularly given (but not limited to) the game supports the use of a grid and miniatures. It is quick to use, easy to understand, does not require a calculator or trigonometry, is difficult to argue about and you can draw it easily on any scale.

The rules as written:

Areas of effect (PHB p.204)

A spell’s effect expands in straight lines from the point of origin.

Cone (PHB p.204)

A cone extends in a direction you choose from its point of origin. A cone’s width at a given point along its length is equal to that point’s distance from the point of origin. A cone’s area of effect specifies its maximum length.

There is also a picture on that page showing the shape produced.

Areas of effect (DMG p.251)

Choose an intersection of squares or hexes as the point of origin of an area of effect, then follow its rules as normal.

Explaining how these rules work together, the process to follow when defining a cone area of effect is:

• Choose an intersection of squares/hexes as the point of origin - i.e. a corner of a square, often the one the caster is standing in;

• Draw a straight line away from the origin of the effect to the range of the spell as stated in the description. This is always in multiples of 5', the size of a standard square on a D&D map, in your example 30', which is 6 standard sized squares/hexes on a grid;

• The width, or more accurately diameter, of the cone at any point along the line above is equal to the distance from the point of effect at that point. As an example this means that at 10', or 2 standard squares, along the line from the origin the cone is 10', or 2 standard squares, wide.

• This implicitly defines a flat bottomed cone, as shown in the diagram on p.204 (though you have to be careful with illustrations, in this case it is accurate). It has a width at it's furthest extent along the straight line equal to the length of that line. A 30' cone will extend 6 squares from its origin and be 6 squares wide at it's fullest extent. All straight lines, no curves.

This precisely describes option 1.

Option 2 and option 3 are definitely not what the RAW describe.

As to encouraging players to cast "off centre", yes of course. A player will probably set the orientation of an area of effect to maximise the number of targets whatever the rules are. They will do it to reduce the amount of unwanted collateral damage as well.

As a related aside, it is important to remember that a grid (if used) is a meta-game guide and does not exist for the characters in the game world in any way, so there is no "correct" orientation for them, just the one that reaches/effects the desired target(s).

DM judgement is required when the cone is not cast parallel to the ground or if the ground is not flat. The DM will have to adjudge what is effected but I strongly suggest you avoid too much discussion and definitely avoid calculators and trigonometry. It should be done as much as possible "by eye" and what is fun and good for the game rather than what is exactly precise. The DM should use the following rule to decide if any parts of the area of effect are blocked:

Areas of effect (PHB p.204)

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover

Note: This answer challenges the question's frame. Believe it or not, there's an official recommendation in dnd-3.5e as to how a DM can handle, among other things, a nuclear explosion, and statistics for such an event are present in official and compatible Wizards of the Coast d20 System products.

While the question defines what features its author would like to see in a D&D 3.5e nuclear explosion, for a DM's nonfantasy needs the Dungeon Master's Guide recommends Wizards of the Coast's own "d20 Modern Roleplaying Game, a D&D-compatible role-playing game for present-day adventures [that] contains a much more extensive treatment of firearms and other high-tech gear" (146; link mine). Assuming similar compatibility, the d20 Future supplement for d20 Modern has statistics for a nuclear missile, but, as that nuclear missile omits some important details, the DM may also want to consult the compatible d20 Future Tech supplement for d20 Future for more information on a nuclear explosion.

d20 Future's nuclear missile is a 1-megaton munition that's "essentially a fusion bomb rigged to a guided rocket" (141) that deals only 16d8 points of damage. (But apparently offering no saving throw—I mean, seriously, you got hit by a nuke! No save for you!) The missile deals generic energy damage, however, so typically resistance to energy doesn't apply, and the missile likely deals full damage to objects (see Energy Attacks on PH 165). Instead of rolling the weapon's damage, d20 Future suggests speeding play by using the weapon's average damage, and in this case that's 72 points of damage. (Darn these pesky time-consuming nuclear weapons!) This is about equivalent to 21d6 points of damage.

At its most basic, a similar explosion—except that it deals fire damage and that there's a Reflex saving throw for half damage—can be created by the 7th-level Sor/Wiz spell delayed blast fireball [evoc] (PH 217) cast by a level 14 wizard who also employs the metamagic feat Sudden Empower (Complete Arcane 83). (The sudden metamagic feats, while they can only be employed once per day, are used in this answer to avoid increasing a spell's slot level.)

But d20 Future assumes a nuclear missile is fired in outer space by a starship at another space-based target and that, if it hits, it deals damage to the entire target, no matter the target's size (and, if it misses, it's somebody else's problem). Thus the nuclear missile has no entry for area. However, d20 Future Tech describes the similarly-themed Fusion Power Core (78) that's available contemporaneously with d20 Future's the nuclear missile. When (no, not if) the Core explodes (because vehicle its powering is destroyed or because its self-destruct is triggered), the Core deals 20d6 points of damage to the pilot of the Core-powered vehicle (or, presumably, anyone else at exactly ground zero) and 16d6 points of damage to all creatures and objects (attended or not is unspecified) in a 120-ft. radius! The text says nothing about saving throws, so this DM assumes there aren't any: it's just boom! and consequences.

The problem, then, is not dealing 16d6 points of damage but dealing that damage to everything in a 120-ft. radius. (By comparison, the spell delayed blast fireball has as its area a relatively meek 20-ft. spread.) There are effects that deal less damage yet affect a wider area (like this answer's 9th-level Corrupt spell apocalypse from the sky [conj] (Book of Vile Darkness 85), especially if modified by the feat Sudden Widen (Complete Arcane 83)) and effects that deal more damage yet typically only to a small area or one target (e.g. the 6th-level Sor/Wiz spell disintegrate [trans] (PH 222), the 8th-level Sor/Wiz spell polar ray [evoc] (PH 262-3)), but only a handful of off-the-shelf spells approach a Fusion Power Core detonation.

One spell that does come close is the 8th-level Clr spell lion's roar [evoc] (Spell Compendium 133) that when cast by a level 17 cleric deals 10d8 points of sonic damage to enemies within 120 ft. of the cleric, but an enemy that succeeds on a Will saving throw suffers half damage, and dealing 56 points of damage like a Fusion Power Core with the roar spell means again using the feat Sudden Empower. (A roar spell deals about 67 points of damage when so modified but only an average of 45 points of damage without using the feat.) The spell also probably doesn't affect objects in the area (unless the DM—perhaps too generously—allows the cleric to designate objects as enemies).

Other spells that might serve as ersatz Core explosions include the more-like-a-cinematic-neutron-bomb 3rd-level Sor/Wiz spell jungle razer [necro] (Spell Compendium 127-8) and the 5th-level Sor/Wiz spell cyclonic blast [evoc] (Spell Compendium 57), yet both are lines not bursts; and the only-if-it's-in-the-water-but-then-it's-awesome 8th-level Sor/Wiz spell maelstrom [conj] (Spell Compendium 135-6), especially if modified by the feat Sudden Empower.

Further, if modified by the feats Sudden Empower and Sudden Widen, a Core explosion can be sort of simulated with the 3rd-level Sor/Wiz spell resonating bolt [evoc] (Spell Compendium 174) yet it's a line and will likely also require employing the feat Sudden Maximize (Complete Arcane 83); or the 5th-level Sor/Wiz spell blast of flame [conj] (Spell Compendium 31) or the 9th-level Moon domain spell moonfire [evoc] (Spell Compendium 144), both of which are cones not bursts.