Doubles All Round! Mystery Cache

For some time I've been carrying round a disco cache; for rather less time I've had the idea for another puzzle; today I found where I could bring them together.

The co-ordinates given are for a parking place from where the cache is about 20-25 minutes walk. There will be mud so you should be prepared! BYOP. The cache is a disco and you might find tweezers helpful. As the final co-ordinates are an average I've given what I think hope is a helpful hint.

The cache is hidden at N 54 56.2N+4E+5S+3W+5X W 001 50.8N+3E+4S+2W+15X.

X is (for some) the celestial follower.

You can check your answers for this puzzle on GeoChecker.com.