In all the cases you cited there is not one that only deals with a fence line. There are no permanent structures erected by you on the easement. There is nothing being stored by you on the easement.
Go and see the attorney and if he tells you that you have a case for AP ask a different attorney. Otherwise you will end up spending a great deal of money and years in litigation only to lose.
Please pardon my stubbornness, but per California Civil Code 323-325, it appears that adverse possession can be argued with the presence of a "substantial inclosure"
or an improvement (permanent structure, etc.).
From Davis v Crump, 162 Cal. 513, 123 P. 294
"During the afternoon of January 8, 1910, between about 1:30 and 6:30 P.M. he inclosed such greater portion of the property in two separate parcels by the construction of substantial five-strand barbed wire fences, with redwood posts, twelve or fourteen feet apart, making two complete inclosures. It cannot well be claimed that these two parcels were not thenceforth each protected by a substantial inclosure (maintained by him), to an extent sufficient to satisfy the requirements of section 325 of the Code of Civil Procedure, as to the kind of possession essential to an adverse possession."
Additionally, how the area enclosed by the fence may have some bearing on the claim, but from Webber v Clarke 74 Cal. 11 (Cal. 1887) 15 P. 431
"The general principle which underlies all this class of cases is, that the acts of dominion must be adapted to the particular land, its condition, locality, and appropriate use. The philosophy of the rule is, that by such acts, the party proclaims to the public that he asserts an exclusive ownership over the land, and the acts which he performs are in harmony with his claim of title."
Thus, I would argue that the historic and current use of the enclosed section as a portion of the yard, to grow and maintain trees and other plants would be "in harmony" for uses of such land in the surrounding neighborhood.
California Civil Code
323.
For the purpose of constituting an adverse possession by any person claiming a title founded upon a written instrument, or a judgment or decree, land is deemed to have been possessed and occupied in the following cases:
1. Where it has been usually cultivated or improved;
2. Where it has been protected by a substantial inclosure;
3. Where, although not inclosed, it has been used for the supply of fuel, or of fencing timber for the purposes of husbandry, or for pasturage, or for the ordinary use of the occupant;
4. Where a known farm or single lot has been partly improved, the portion of such farm or lot that may have been left not cleared, or not inclosed according to the usual course and custom of the adjoining country, shall be deemed to have been occupied for the same length of time as the part improved and cultivated.
(Enacted 1872.)
324.
Where it appears that there has been an actual continued occupation of land, under a claim of title, exclusive of any other right, but not founded upon a written instrument, judgment, or decree, the land so actually occupied, and no other, is deemed to have been held adversely.
(Enacted 1872.)
325.
(a) For the purpose of constituting an adverse possession by a person claiming title, not founded upon a written instrument, judgment, or decree, land is deemed to have been possessed and occupied in the following cases only:
(1) Where it has been protected by a substantial enclosure.
(2) Where it has been usually cultivated or improved.
(b) In no case shall adverse possession be considered established under the provision of any section of this code, unless it shall be shown that the land has been occupied and claimed for the period of five years continuously, and the party or persons, their predecessors and grantors, have timely paid all state, county, or municipal taxes that have been levied and assessed upon the land for the period of five years during which the land has been occupied and claimed. Payment of those taxes by the party or persons, their predecessors and grantors shall be established by certified records of the county tax collector.
(Amended by Stats. 2010, Ch. 55, Sec. 1. (AB 1684) Effective January 1, 2011.)