Well, first of all I think that ship design was also changing in time among different cultures in Middle Earth. For example it seems that even elves developed a bit their designs, the White Ship build by Cirdan for transporting Ring-bearers appears to be more advanced than viking-like:
Then Círdan led them to the Havens, and there was a white ship lying, and upon the quay beside a great grey horse stood a figure robed all in white awaiting them. As he turned and came towards them Frodo saw that Gandalf now wore openly upon his hand the Third Ring, Narya the Great, and the stone upon it was red as fire. Then those who were to go were glad, for they knew that Gandalf also would take ship with them.
Then Frodo kissed Merry and Pippin, and last of all Sam, and went aboard; and the sails were drawn up, and the wind blew, and slowly the ship slipped away down the long grey firth; and the light of the glass of Galadriel that Frodo bore glimmered and was lost. And the ship went out into the High Sea and passed on into the West, until at last on a night of rain Frodo smelled a sweet fragrance on the air and heard the sound of singing that came over the water. -RotK, Book VI, Ch 9, The Grey Havens
It seems there are multiple sails (and masts apparently). I myself have always pictured those numenorean ship and later elven ones (post-Vingilot design which also appears to have more than one sail) as various types of so called "tall ships" (with Numenorean ones it brings in mind colonial empires and their treasure fleets, cause as we are told in writings, great riches were brought from continent and inhabitants of Numenor "build ever greater ships", also later fleets of Gondor also had large ships of great drought that filled the elven havens for war with Angmar). Also it appears that even before First Age, Teleri elves were skilled in making ships, as the unknown number of them (called "fairiest" sailing vessels) transported thousands of noldorin warriors with their families and great store of goods, even horses, later the feanorian faction who took the ships was able to gift Fingolfin's host, who lost much horses in crossing of Helcaraxe, with many horses enough to form horsed troops of Hithlum when bred accordingly, most likely elven craftsmen took their tools, other possessions were taken even treasures from Aman, Finrod had many jewels, but those things wouldn't take much place aboard :), possibly elves took hunting hounds too, if example of Celegorm who went with his horse-huge Huan (as Luthien was able to ride him) is anything to go by.
Also brief description of Alcarondas, Castle of the Sea many masted, brings in mind galleons or something alike (in History of Middle Earth texts in History of the Akallabeth there is mentioned that Ar-Pharazon envisioned a Great Armament fleet that would surpass the one he brought to subdue Sauron like a ,,great galleon of Numenor surpasses a fisherman's boat" (The Peoples of Middle-Earth, HoME Vol 12, Part 1, Ch 5, The History of the Akallabêth) though it's difficult to say whether this text can be taken as canon. Corsairs of Umbar had those ,,fifty great ships" and ,,smaller vessels beyond count" and I thought that the dromunds were those smaller, and 50 great ones could be those ships of great drought but still no clue how they would look like. It's possible that each nation and culture would have it's own specific type of ship Haradrim would have their own (there are other havens in Harad and not all belong to Umbar), Gondorians would be one of the most advanced in regard to their numenorean heritage, elves have Cirdan stated to be the most skilled and inventive shipbuilder, so elven ships might come in many varieties depending on their purpose (it is speculative but he could have put some elven magic in them, as Tolkien stated in one of the letters ships going to Undying Lands were "specially made and hallowed" for such a journey).
The example of the Lohtlorien boat is rather a simple river barge, Galadhrim had their own harbor and possibly sent scouts in boats to spy out the land or to transport troops for military operations (seen mostly in their campaign against Dol Guldur), Wood Elves of northern Mirkwood also used many boats and rafts for both civilian and military uses (and there were specialized raftsmen...err raft elves) like shipping goods up and down the river, they had their harbors and small river ports with villages of elves living by Forest River, Esgaroth and Dale had whole fleets of large boats, small ships and great barges to travel up and down the Celduin/river Running and Long Lake (so vast that standing on one shore you can barely see the other one as a thin line in narrower spot) and depending on size and exact course of waterways ships could be varying in look from simple viking longboats with single mast (drakkars or knarrs) to more elaborated galleys with multiple masts and sails, two decked, maybe standard design for river traffic could be a cog (or maybe a bit like herring buss only going on river instead of the sea, galleys seems also a good possibility, with small draft galleys could travel up rivers). Overall though it's based mostly on speculation and we can't say much on the topic.