[Maédhros]

The Silm indeed states "Now the Elves made many rings". Twenty rings (1+3+7+9) doesn't sound 'many rings' to me. I always figured there were more rings than these. Bilbo's ring could have been one of these lesser rings, making it much harder for Gandalf to find out which ring Bilbo's indeed was.

He could have done exactly the same thing that he did later on. Go to Minas Tirith and look for clues about the Ring that Isildur wore. Simple.
He didn't have to wait for 59 years to do it.
Twenty rings sounds "many" to me.

As to Isildur, The Disaster of the Gladden Fields in the Unfinished Tales says: "No trace of his body was ever found by Elves or Men." suggesting that they did indeed search for him. It also says that "his mail, helm, shield and great sword (but nothing else) had been found", further suggesting he was searched for.

It seems to me that you need to keep on reading the other paragraphs of The Disaster of the Gladden Fields

Long afterwards, as the Third Age of the Elvish World waned and the War of the Ring approached, it was revealed to the Council of Elrond that the Ring had been found, sunk near the edge of the Gladden Fields and close to the western bank; though no trace of Isildur's body was ever discovered. They ere also then aware that Saruman had been secretly searching in the same region; but though he had not found the Ring (which had long before been carried off), they did not yet know what else he might have discovered.
But King Elessar, when he was crowned in Gondor, began the re-ordering of his realm, and one of his first tasks was the restoration of Orthanc, where he proposed to set up again the palantir recovered from Saruman. Then all the secrets of the tower were searched. Many things of worth were found, jewels and heirlooms of Eorl, filched from Edoras by the agency of Wormtongue during King Théoden's decline, and other such things, more ancient and beautiful, from mounds and tombs far and wide. Saruman in his degradation had become not a dragon but a jackdaw. At last behind a hidden door that they could not have found or opened had not Elessar had the aid of Gimli the Dwarf a steel closet was revealed. Maybe it had been intended to receive the Ring; but it was almost bare. In a casket on a high shelf two things were laid. One was a small case of gold, attached to a fine chain; it was empty, and bore no letter or token, but beyond all doubt it had once borne the Ring about Isildur's neck. Next to it lay a treasure without price, long mourned as lost for ever: the Elendilmir itself, the white star of Elvish crystal upon a fillet of mithril that had descended from Silmarien to Elendil, and had been taken by him as the token of royalty in the North Kingdom. Every king and the chieftains that followed them in Arnor had borne the Elendilmir down even to Elessar himself; but though it was a jewel of great beauty, made by Elven-smiths in Imladris for Valandil Isildur's son, it had not the ancientry nor potency of the one that had been lost when Isildur fled into the dark and came back no more.
Elessar took it up with reverence, and when he returned to the North and took up again the full kingship of Arnor Arwen bound it upon his brow, and men were silent in amaze to see its splendour. But Elessar did not again imperil it, and wore it only on high days in the North Kingdom. Otherwise, when in kingly raiment he bore the Elendilmir which had descended to him. "And this also is thing of reverence," he said, "and above my worth; forty heads have worn it before."
When men considered this secret hoard more closely, they were dismayed. For it seemed to them that these things, and certainly the Elendilmir, could not have been found, unless they had been upon Isildur's body when he sank; but if that had been in deep water of strong flow they would in time have been swept far away. Therefore Isildur must have fallen not into the deep stream but into shallow water, no more than shoulder-high, Why then, though an Age had passed, were there no traces of his bones? Had Saruman found them, and scorned them – burned them with dishonour in one of his furnaces? If that were so, it was a shameful deed; but not his worst.

Isildur was slained in year 2 of TA. It is in 2463 when Déagol the Stoor finds the One Ring, and is murdered by Sméagol.
Then we find out that Saruman begins to search the Gladden Fields at 2851 TA.

If what you say is true, then both the Elves and Men who searched for the remains of Isildur must be very incompetent or clueless.
Look, Déagol found the Ring in 2463 TA, meaning that 2461 years had passed from the death of Isildur, and Saruman found items belonging to Isildur in 2851 TA. There had passed 388 years since Déagol had found the ring.
Are you telling me that in 2849 years, the good guys could not have found those things that Saruman did? Please.