Relief from cart path on a hill

I sent this question to the USGA, based on a situation from my last round; we'll see what they say in about a month (if that), but I thought I'd let you guys have a try as I'll be playing the same course before the USGA's likely to get back to me.

EDITED:

A player's ball has come to rest in bounds against the outside edge (opposite to the fairway) of a formed concrete cart path running roughly parallel to the line of play, which is an immovable obstruction. This cart path travels perpendicular to the incline of a hill rising away from the fairway, such that the nearest point of relief from the current lie (the closest point perpendicular to the desired line of play at which the cart path no longer impedes the player's stance or swing) is further up the incline. The player takes relief under Rule 24-2b(i) by dropping the ball at this nearest point of relief. The ball hits the turf and rolls back down the incline, again coming to rest against the outside of the cart path, thus requiring a re-drop under 20-2c. This has the same result, and again under rule 20-2c, the ball is required to be placed at the spot; it still rolls, and rolls again when replaced under 20-3, and no suitable point within a clublength of the nearest point of relief can be found where the ball will remain where it is placed.

The player and his fellow-competitors concede that attempting to take relief at the determined point is futile. So, the player determines a new "nearest point of relief" to be on the opposite side of the cart path, and drops a ball at that point. The ball then rolls down the incline onto the fairway (not nearer the hole), coming to rest more than two clublengths away from the point of relief, and thus requiring a re-drop under 20-2c; however, the situation is similar, as whether dropped or placed the ball is almost certain to roll into a position violating 20-2 or 20-3. A fellow-competitor also says that this is a violation of Rule 13-2 as, in taking relief, the player has moved his ball from the rough to the fairway, thus dramatically improving its lie and the line of play beyond what is reasonable to allow in taking relief from the obstruction.

The player and fellow-competitors decide on two solutions they feel to be equitable: first, to allow the player to play the ball as it now lies under penalty of one stroke; or second, to return the ball to its original lie, and then use the procedure under Rule 28b (determining a point on a line between the lie and the hole and behind the current lie) to define the "nearest point of relief" at which the player may take relief under 24-2b(i) without penalty. The player is given the choice and chooses the latter, and the ball is dropped successfully at a point 25 yards behind the initial lie, inside the cart path, and played from that spot to completion of the hole.

Did the players proceed correctly? Would it also have been correct to choose the first option?

EDIT: edmastermind29's answer to the question as originally stated is completely true and correct; the ball should be placed at the nearest point of relief if after both a drop and re-drop the ball comes to rest in a spot where the obstruction interferes.

However, Rule 20-3d states:

If a ball when placed fails to come to rest on the spot on which it was placed, there is no penalty and the ball must be replaced. If it still fails to come to rest on that spot:

(i) except in a hazard, it must be placed at the nearest spot where it can be placed at rest that is not nearer the hole and not in a hazard;

We may assume, for the purposes of this question, that the hill is steep enough that the ball will roll when placed as well as when dropped; that the crest of the hill is out of bounds; and thus that the "nearest spot where the [the ball] can be placed at rest that is not nearer the hole" is at the edge of the fairway near the bottom of the incline (this really was the situation; the hill, being mostly in the rough, was not being watered due to drought conditions, and as a result what grass there was was thin, dormant and providing virtually no rolling resistance). Thus, the situation would have been the same after the correct procedures were followed.

Rule 13-2 states:

A player must not improve or allow to be improved:

• the position or lie of his ball
• "(i) except in a hazard, it must be placed at the nearest spot where it can be placed at rest that is not nearer the hole and not in a hazard;" -- I interpret this to mean that the "nearest spot," although on the fairway, is the "nearest point of relief" and it may be placed on the fairway as the spot satisfies both not being near the hole and not being in a hazard.
– user527
Aug 1, 2012 at 19:13

If the ball is re-dropped at "the closest point perpendicular to the desired line of play at which the cart path no longer impedes the player's stance or swing" but once again satisfies rule 20-2c of when to re-drop, the end of rule 20-2c states:

If the ball when re-dropped rolls into any position listed [in rule 20-2c], it must be placed as near as possible to the spot where it first struck a part of the course when re-dropped.

Then, the ball must be placed given the following:

A ball to be placed under the Rules must be placed by the player or his partner.

Did the players proceed correctly? Would it also have been correct to choose the first option?

No. The options should have not been considered, let alone determining a new "nearest point of relief," as the ball would have been placed "as near as possible to the spot where it first struck a part of the course" after a re-drop.

• +1 because you are absolutely correct, but see edit. Aug 1, 2012 at 18:47
• @KeithS Did the USGA answer your inquiry yet? I am interested to hear what they say.
– user527
Aug 6, 2012 at 15:39
• Exactly the same as you. However, I didn't give them the same update as I made here, so I'm still interested in what would be the proper procedure if neither dropping nor placing, neither above nor below the cart path, results in a situation that follows either of the major Rules. Aug 6, 2012 at 18:55