It didn’t “take over”. That premise is incorrect. Species has always been singular, and the old plural specieses is obsolete.

Obsolete or erroneous specie

The form specie to mean what we now mean by species—that is, “kind”—the OED says is:

Now Obsolete except as erroneous singular of species n. 10.

It provides such citations for that sense now held to be erroneous in current use as these:

• 1711 London Gaz. No. 4874/4
  To prepare a List of each respective Specie [of bills] which they intend to Subscribe.
• 1738 G. Smith Curious Relations II. 558
  Such Men who are Plagues to their own Specie.
• 1747 Fool (1748) II. 141
  Our Hero made Divinities, though of a peculiar Specie.
• 1800 C. Sturt in Naval Chron. 4 396
  A very large specie of gull.
• 1810 Splendid Follies III. 193
  Such is the specie of game after which Nettletop is now in search.
• 1858 in J. R. Bartlett Dict. Americanisms (1859) 432
  The size of the trap,..and the nature of the bait, depends upon the specie of the animal hunted for.
• 1980 Daily Tel. 22 Jan. 11/2
  Castrated rats and other animals live longer than normal creatures of the specie.
• 1980 Pan Am Clipper Oct. 48/1
  Is he [sc. man] descended directly from apes, or is he a specie that evolved from an entirely new..branch of the primate tree?

It seems clear to me that the old ones are obsolete and the newer ones erroneous, but I don’t know how to assign which of the obsolete vs. erroneous label to citations more recent than 1800 but less recent than 1980. If you made me guess, I would guess obsolescence occurred sometime during the 19th century. I don’t know how to determine that though.

Species has always been singular

Indeed, species has always been singular, just as it normally is today. The obsolete versions cited above were always a rare use even in the 1700s. The OED gives this for its etymology:

Latin speciēs (ablative singular speciē specie n.) appearance, form, kind, etc., < specĕre to look, behold; hence also German species, spezies. Within the Romanic languages the word is represented by Italian specie, spezie, Spanish especie (and especia), Portuguese especie (and especia), Old French espece (French espèce) and espice (French épice): see spece n. and spice n.

Indeed all the Latin fifth-declension nouns worked this way. See also series versus in serie.

And here are some of its earlier citations:

• 1551 T. Wilson Rule of Reason sig. Bvj
  Species is a common word that is spoken of many whiche differ only in number, as manne is spoken of Socrates,..and of euery proper name belonging to any man. As Socrates is a man.
• 1559 P. Morwyng tr. C. Gesner Treasure of Euonymus 400
  An other very good wine with the same species, but in other weight.
• 1561 T. Hoby tr. B. Castiglione Courtyer iii. sig. Cc.iii
  Both the one and the other is conteined vnder the Species of Homo.
• 1567 J. Jewel Def. Apol. Churche Eng. iii. v. 343
  What adoo was made in daily disputations..aboute Genus and Species, and the reste of the Vniuersals.
• 1608 E. Topsell Hist. Serpents 126
  Some haue taken the word Crocodilus for the Genus, and the seuerall Species, they distinguish into the Crocodile of the Earth, and the water.
• 1617 F. Moryson Itinerary i. 275
  With covenant to deliver him by his Factor the same [coins], both in the Species or Kind, and in the number.
• a1618 W. Raleigh Prerog. Parl. 58
  If all be content to pay upon moderation and change of the Species.
• 1629 W. Prynne Church of Englands Old Antithesis 98
  This kind of argument from euery indiuiduall to the speecies will not hold.
• 1660 R. Coke Justice Vindicated ɪɪ. 26
  If the Scriptures be true,..that since Adam..the species of Mankind was continued by generation.
• 1660 tr. I. Barrow Euclide's Elements ᴠɪ. 119
  The angles C and F are not of the same species or kind.
• 1668 Bp. J. Wilkins Ess. Real Char. ɪɪ. i. §3. 26 That common nature which is communicable to several Individuals, is called Species, Sort or special kind.
• 1690 J. Locke Ess. Humane Understanding ɪɪɪ. vi. 211
  The Individuals that are ranked into one Sort, called by one common Name, and so received as being of one Species.
• 1730 P. Miller Gardeners Dict. at Leontopetalon
  We have but one Species of this Plant in the English Gardens.
• 1753 Chambers's Cycl. Suppl. at Specific
  The torpedo maculosa, and non maculosa, seem to express two species different only in the spots.
• 1843 J. S. Mill Syst. Logic I. ɪ. vii. §3
  In this popular sense any two classes one of which includes the whole of the other and more may be called a genus and a species.

That shows that species has always been singular.

Plural †specieses is long dead

During the 1600s–1800s the now-extinct form †specieses was sometimes used for the corresponding plural, but today its plural is the same as its singular has always been. Here are some of those specieses citations for the plural:

• 1644 K. Digby Two Treat. ɪ. xxxviii. 329
  If there be aboundance of specieses of any one kind of obiect then strong in the imagination.
• 1644 K. Digby Two Treat. ɪ. ii. 14
  There remaineth no more to be said of this subiect, but to enumerate the seuerall specieses of Quantity.
• 1792 Ld. Monboddo Orig. & Progress of Lang. ix. 110
  These perfect ideas of Plato are no other than the specieses of things which were held by Aristotle to exist in the mind of the deity.

Thus species is not the same word as specie, and never has been so outside of a few scattered obsolete or erroneous uses.

Visits “received in specie, paid in individuo”

The distinct word specie meaning a coin or coined money is used almost exclusively in the Latin phrase in specie for “in kind” where it takes the ablative grammatical case inflection. The phrase was often set in italic to indicate this.

• 1551 T. Cranmer Answer S. Gardiner 182
  As vnto the Jewes Christe was geuen in figures, so to vs he is gyven in specie, that is to say, in rei veritate, in his very nature.
• 1562 W. Turner 2nd Pt. Herball f. 93ᵛ
  Pitiusa is iudged to differ in spicie or kynde from the cypresse spourge.
• 1620 H. Wotton Dispatch from Vienna 7 Sept. in Reliquiæ Wottonianæ (1685) 501
  Whether visits of respect..being received in specie, should be paid in individuo.
• a1637 B. Jonson Timber 2714 in Wks. (1640) III
  They differ; but in specie: either in the kinde is absolute.

For the freestanding, non-Latin use, we see:

• 1671 in 9th Rep. Royal Comm. Hist. MSS (1883) App. II. 13/2
  Unpurged brown [sugar], being the specie of the country [Barbadoes], pays for the exports from the kingdom.
• 1710 True Acct. Last Distemper T. Whigg ɪɪ. 19
  A Bung-Cart [perh. read Dung-Cart], drawn by an Ox and an Ass, and laden with Specie and Exchequer Bills, to purchase Country Votes.
• 1749 T. Smollett tr. A. R. Le Sage Gil Blas IV. x. x. 67
  I sometimes kissed the species, and contemplated the different pieces with..rapture.
• 1864 F. C. Bowen Treat. Logic ix. 274
  Money may mean either specie, or bank-notes, or currency consisting of a mixture of these two.

Summary

So singular species did at no point ever “take over” from some singular specie. It has always been there.