It looks like the verbiage has changed over the last year, and give more clarity now:
They flit around you to a distance of 15 feet for the duration
The biggest difference is it does not say up to 15 feet. It says to a distance of 15 feet. That is a hard number that does not sound like it will ever extend past 15 feet the way it is written.
Things to consider:
- Spirit Guardians Range:
Range: Self (15-foot radius)
- AOE Rule:
A spell's description specifies its area of effect, which typically has one of five different shapes: cone, cube, cylinder, line, or sphere. Every area of effect has a point of origin, a location from which the spell's energy erupts. The rules for each shape specify how you position its point of origin. Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
15 foot radius implies a circle, and since the range of the spell is Self, YOU are the point of origin. If you are standing on a hex or square, you would take up the space of 1 full square or hex, and extend 15' in all directions from one of the intersections of your choice in your occupied space per the DMG, page 251:
Choose an intersection of squares or hexes as the point of origin of an area of effect, then follow its rules as normal. If an area of effect is circular and covers at least half a square, it affects that square.
There is no verbiage that says the footage is extended if you are larger. You can learn more about circles or spheres cast on grids here.
That being said to answer your question: No, the radius of the Spirit Guardians spell does not depend on the caster. It is always a 15' radius circle (circle shape implied with radius). However the point of origin on the grid can alter the "reach" of the spell.
It is always 15' from the point of origin which is yourself, and will be the center of said origin.