edit to supply link:
Grauniad The fist usage the OED2 traces is to c.1250 and is the ordinary one you might expect:
1. Characterized by abundance, possessing or affording copious supply; abundant, plentiful, full. In addition it traces the pejorative extension of that meaning to much later (1633) and calls it obsolete:
†b. Growing abundantly, rank in growth. Obs.They then trace umpteen other variants – nearly all the pejorative senses are marked obsolete.
2. Of the body, etc.: Full and plump, fat, well-grown; in a bad sense, over-grown. Obs.
†b. Overfed, surfeited. Also fig. Obs.
†c. App. used for: Lustful, ‘rank’. Obs.
3. Of food: Satiating, ‘filling’, tending to cloy or surfeit; also, coarse, gross, unsuited to a dainty palate. Obs.
†b. Having a sickly or sickening taste; tending to cause nausea. Obs.
†c. fig. Cloying, satiating, wearisome from excess or repetition. (Cf. sense 7.) Obs.
4. Offensive to the sense of smell: a. Strong-smelling, of strong, rank, or overpowering odour. b. Foul-smelling, stinking. Obs.
5. Offensive to the senses generally; physically disgusting, foul, or loathsome. Obs.
6. Offensive to normal tastes or sensibilities; exciting aversion or repugnance; disgusting, repulsive, odious. ? Obs. exc. as in sense 7.
†b. Morally foul, filthy, obscene. Obs.
7. Of language, style, behaviour, etc.: Offensive to good taste; esp. offending from excess or want of measure or from being ‘over-done’. Now chiefly used in reference to gross or excessive flattery, over-demonstrative affection, or the like.
1663 Bp. Patrick Parab. Pilgr. 201, I never heard anything so fulsome from the mouth of man; and found my self+impatient of such silly stuff. 1692 Bentley Boyle Lect. vi. 189 They were puffed up with the fulsome Flatteries of their Philosophers and Sophists. 1702 Rowe Tamerl. iii. i. 1081 Bear back thy fulsom Greeting to thy Master. 1762 Goldsm. Cit. W. xviii, Concealed disgust under the appearance of fulsome endearment. 1782 J. Warton Ess. Pope II. xii. 338 This fawning and fulsome court-historian. 1784 Cowper Task vi. 289 The fulsome cant And pedantry that coxcombs learn with ease. 1802 M. Edgeworth Moral T. (1816) I. 226 The fulsome strains of courtly adulation. 1873 Symonds Grk. Poets vi. 169 Pindar was never fulsome in his panegyric. 1874 Helps Soc. Press. xiii. 778 This fulsome publicity I have described.
b. quasi-n.Since virtually all the pejorative associations have lapsed long ago it's not surprising that it tends to be used largely in the (earliest) positive sense, is it? I’m afraid I think you may have lost this battle some centuries ago mate!