Voldemort's language would have suggested to Dumbledore that those other experiments were unsuccessful.
I've argued elsewhere that Voldemort did indeed try to achieve immortality in other ways, on the basis of the quotes in the question. I believe that successive experiments in various forms of Dark Magic were part of the reason why Voldemort's face and overall appearance became so disfigured. The Horcruxes played no small part in this transformation; losing your soul piece by piece is certainly going to have an impact on your appearance. But I agree that the words "one or more of my experiments" suggests multiple attempts to achieve immortality. The Horcruxes were one of many things that Voldemort tried. They just so happened to be the only method which was successful.
Of course, we don't know what those experiments were. They're never referred to again. However, I think that we can establish why Dumbledore was reasonable to suppose that the Horcruxes were Voldemort's only credible defence against mortality.
Firstly, Dumbledore is pretty open about the fact that his assessments of Voldemort are guesswork. He recognises that he could be wrong about how to defeat him, and how huge the consequences of making a wrong judgement could be.
“I told you everything I know. From this point forth, we shall be leaving the firm foundation of fact and journeying together through the murky marshes of memory into thickets of wildest guesswork. From here on in, Harry, I may be as woefully wrong as Humphrey Belcher, who believed the time was ripe for a cheese cauldron.”
“But you think you’re right?” said Harry.
“Naturally I do, but as I have already proven to you, I make mistakes like the next man. In fact, being - forgive me - rather cleverer than most men, my mistakes tend to be correspondingly huger.”
(Half-Blood Prince, Chapter 10, The House of Gaunt).
When talking about Horcruxes specifically he is similarly hesitant.
“So, the other Horcruxes?” said Harry. “Do you think you know what they are, sir?”
“I can only guess,” said Dumbledore.
(Half-Blood Prince, Chapter 23, Horcruxes).
All of Dumbledore's reasoning about the Horcruxes were educated guesses, formed from deductions about Voldemort's behaviour and his past.
However, it was reasonable for Dumbledore to presume that the Horcruxes were Voldemort's sole form of defence. Voldemort's language when describing his immortality is remarkably vague.
"You know my goal - to conquer death. And now, I was tested, and it appeared that one or more of my experiments had worked..."
(Goblet of Fire, Chapter 33, The Death Eaters).
I think the key word there is "experiments". Voldemort has been experimenting with various forms of immortality, and isn't even clear himself (at least openly to his followers) which one of those worked. Voldemort's language is much more consistent with a series of desperate attempts to achieve immortality, one of which, luckily enough, happened to come off than a series of successful back-up plans, all of which made him immortal. The "or more" in his statement is probably a distraction. Of course, with an experiment you can't really rule out that something you tried worked without you knowing. Voldemort could've pulled off a mystery spell that gave him immortality without realising it was successful. But this isn't at all likely - and Dumbledore knew this. Methods of attaining immortality aren't exactly two a penny. Voldemort would've tried everything he could've, since his life goal (stated in the quote) is to become immortal and to cheat death. But it's only logical to assume that these desperate attempts didn't come to anything. Obviously, as far as both Voldemort and Dumbledore were concerned, the only way to really test whether an immortality device works is to try to die, which is something Voldemort would never willingly do. The success rate of these experiments was unknown until they were tested. This only happened once, and they worked. This was all Voldemort and Dumbledore knew for certain.
Nevertheless, logic suggested that Horcruxes were by far the most likely option. Voldemort was ripped from his body when the Avada Kedavra spell hit him. We're told that this spell is unblockable but clearly any magic which Voldemort tried which made him invulnerable from Killing Curses didn't work. He was hit by a Killing Curse, and it killed him, just as it would've done for anyone else. Dumbledore knows this, and he also knows that it's likely that the only surviving part of Voldemort from the Godric's Hollow attack is his soul. Dumbledore would've deduced that Voldemort was an incorporeal spirit both from the rumours he heard from Albania and from the evidence of Voldemort's activities in Philosopher's Stone. Voldemort's form is consistent with a soul, which suggests that the magic Voldemort used was magic that protected his soul, which suggests Horcruxes. Any other magic which was about protecting the body can be ruled out.
Remember that the Slughorn memory gives Dumbledore proof that Voldemort was pursuing Horcruxes as an immortality device from a very young age. Voldemort was transfixed with the idea using Horcruxes to create a seven-part soul ever since he was a schoolboy. The diary also clearly suggested to Dumbledore that Voldemort followed through on his plans and had actually created at least one Horcrux. All of this was irrefutable evidence. In contrast, these other mystery experiments are only mentioned in passing on one occasion. Dumbledore didn't have any evidence to go on regarding other methods of immortality. He didn't have much of a reason to devote his limited time to investigating other things that Voldemort tried which were probably unsuccessful, based on zero evidence. Instead, he focused on the Horcruxes, which he definitely knew that Voldemort had adopted.
Besides, Dumbledore believed that, even if he was successful in gaining immortality by another route, Voldemort would be unwilling to utilise these methods when they had drawbacks.
"I believe that he would have found the thought of being dependent, even on the Elixir, intolerable. Of course he was prepared to drink it if it would take him out of the horrible part-life to which he was condemned after attacking you, but only to regain a body. Thereafter, I am convinced, he intended to continue to rely on his Horcruxes. He would need nothing more, if only he could regain a human form. He was already immortal, you see...or as close to immortal as any man can be."
(Half-Blood Prince, Chapter 23, Horcruxes).
Dumbledore clearly viewed the Horcruxes as Voldemort's primary method of attaining immortality. Any other devices, such as the Philosopher's Stone, were only useful to him as a way of getting a new body. They weren't substitutes for the Horcruxes, which were always Voldemort's main and indeed only defence against death.
Even if Voldemort had other secrets about immortality which Dumbledore didn't know about, Voldemort's Horcruxes still had to be destroyed anyway. This was a big enough task without bringing in other external problems.
So I think that
Was Dumbledore simply dealing with what he knew and hoping that it would all work out?
is the best-supported explanation from the books. Nevertheless, I don't think that Dumbledore was unreasonable in ignoring the line about experiments. There wasn't really much to go on other than a remark made in passing. Those experiments clearly didn't protect Voldemort from Avada Kedavra so it was reasonable to focus on destroying the Horcruxes rather than chasing unpromising leads.