I am trying to get a precise set of measurements for coneshaped areas of effect so that I can craft a physical template to use as an overlay when playing with miniatures. I want to get it right the first time.
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. These are “good enough” when playing without a grid, or when only needing a gridshaped approximation of the area of effect, but they are causing me difficulties with crafting an accurate physical template.
There are three incompatible interpretations of the maximum length of a cone (PHB, p. 204; emphasis mine):
A cone's area of effect specifies its maximum length.
… which each lead to slightly different template constructions (using a 30' length as the working example):

You can use the maximum length as the centreline of an isosceles triangle.
This would give a template that has a centreline 30' long, but edges beyond the “maximum” length that are ~33.5' long. The end of the area of effect would be a flat plane. This shape would encourage players to aim offcentre to use the “bonus” length offered by the edges.

You can use the maximum length as the edges of an isosceles triangle.
This would give a template with no portion farther than the maximum away, but with a centreline length that is only ~27.8'. The end of the area of effect would be a flat plane. This shape would motivate players to do offcentre aiming in order to get full use of the maximumlength edges of the template.

You can use the maximum length as a radius of a conical section of a sphere (a spherical cone).
This would result in a template with a rounded end, with all points on that arc exactly the maximum length away from the point of origin.
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?
Best Answer
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:
and
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)
Cone (PHB p.204)
There is also a picture on that page showing the shape produced.
Areas of effect (DMG p.251)
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 metagame 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)