Therefore, you cannot hit any target between 0' to 250', but are free to hit any target 255' to 500'.
While I'll agree that the threatened area is doughnut-shaped, I disagree on the inner radius. All references that I can find to being unable to strike enemies that are too close give the area as either “within your natural reach” or “adjacent.” There's nothing to indicate that increasing the outer radius of the doughnut would have any effect on the inner radius.
A reach weapon is a melee weapon that allows its wielder to strike at targets that aren’t adjacent to him or her. Most reach weapons double the wielder’s natural reach, meaning that a typical Small or Medium wielder of such a weapon can attack a creature 10 feet away, but not a creature in an adjacent square. A typical Large character wielding a reach weapon of the appropriate size can attack a creature 15 or 20 feet away, but not adjacent creatures or creatures up to 10 feet away.
While I would prefer to have a third example, two examples is enough to make a conjecture. at 10', you cannot hit anything at 0'-5'. At 20', you cannot hit anything 0-10'. We can therefore extrapolate that whatever the threat radius, the area that you cannot hit is half that.
To further prove my point with data that indirectly proves my position, I would direct you to DMG 308-310 where they have the diagrams of Space and Reach. It does not specifically state that you cannot threaten the smaller area, but it does show by way of shading that the "normal" threat range is different from the "reach" threat range.
I will admit, I am on shaky ground here, but in the absence of information to the contrary, I must assume that all reach weapons, unless specifically stated otherwise in the text, have a doughnut hole in the center equal to x1/2 the threat range of your reach where the attack cannot threaten.
Assuming you wish to continue with your 500' rope improvised weapon idea...
Improvised Weapons (Ex): While bottles and tankards are a drunken master’s preferred improvised weapons, he can
use furniture, farm implements, or nearly anything else at hand to attack his foes. A drunken master’s improvised weapon deals as much damage as his unarmed strike plus an extra 1d4 points.
That means your rope does whatever your unarmed strike does.
So, you need a necklace of natural weapondry, and a pair of bracers of striking. As I have explained elsewhere, you could add a +1 to your rope and tack on an additional +19 in WSAs.
Note the underlined word. While WSA's like Flaming would work, I don't think ones like Brilliant Energy would.
A weapon has an enhancement bonus. Your logic states that the +1 to hit would allow +1 damage, but not +1 to hit.
If you accept that an EB would affect both Damage and To hit...
In addition to an enhancement bonus, weapons may have special abilities. Special abilities count as additional bonuses for determining the market value of the item, but do not modify attack or damage bonuses (except where specifically noted). A single weapon cannot have a modified bonus (enhancement bonus plus special ability bonus equivalents) higher than +10. A weapon with a special ability must have at least a +1 enhancement bonus.
While the bold text indicates that all WSAs are an additional bonus, the italic text would seem to indicate that it only applies to cost. However, from a legal standpoint, a prepositional phrase is not a limiter to exclusion unless it includes the world "ONLY". We cannot determine the author's original intent. Is the "For..." to be an example, or the only case where this is to be applied?
When it comes to reading legal documents, the default is clear. Without the limiter, the original statement considers the prepositional phrase to be an example. Therefore, by RAW, all WSAs are bonuses.
If you accept that EBs would modify the rope's Damage and To Hit, then you must accept that all WSAs, regardless of modifying damage or not, would apply to the rope, as allowed by the individual description of the WSA.
Now then, why do I believe that "as much
damage as his unarmed strike" would include WSAs?
There are examples of items using the monk's Unarmed strike as a base elsewhere. Ward Cestus and Battle gauntlets come to mind.
Since I have a number of other sources indicating that the WSAs transfer through, I see no reason to assume that "damage" is just ill defined. If I paralyze my enemy, have I damaged him? If I drain him of con, have I damaged him? Brilliant energy doesn't damage my enemy, but only is a damage limiter. I cannot damage objects, only living things. Why would that not modify my damage? Since I cannot harm constructs and undead with it, you might assume that being a "damage modifier" it would work.
See? It gets fuzzy. I can make all sorts of arguments for various WSAs based on the word "Damage". So, it becomes far simpler to just state that all WSAs effect the rope, then to try and figure out exactly what the word means.