How is it even possible to travel that far and such a long time by mere canoe?

While they did use canoes, that "mere" is perhaps misplaced. The canoes used in Polynesia for long-distance voyaging were large. They were usually double-hulled (single-hulled outrigger canoes and triple-hulled canoes were also used), and could be about 20m long and 6m wide (across both hulls). This is longer than and as wide as Columbus's caravels Pinta and Niña. These "mere" canoes could carry over 5 tons of passengers and cargo, which while less that the capacity of caravels, is still substantial.

The main propulsion was by sail, and modern replicas of Polynesian voyaging canoes can reach speeds of 5-6 knots under sail with good winds (similar to the performance of modern replicas of caravels, but achieved with about a quarter of the sail area). The replica Hōkūleʻa has amply demonstrated the capability of these vessels, sailing from Hawai's to Easter Island and back, via the Marquesas, in 1999-2000, and circumnavigating the world in 2014-2017 (a similar time to Magellan's voyage, but without that voyage's death toll of over 90%).

As for suicide missions, the likely approach was to first explore, only going as far as supplies would allow a return voyage. Land could be located even when still out of sight by watching birds and by the disruption of waves by islands (a practical use for the diffraction of waves!). Techniques such as this could greatly increase the chance of finding an island. Once land was found, and found to be suitable for settlement, a larger expedition to colonise the new island(s) could sail.

Further reading and references:

The replica Hōkūle‘a: http://www.hokulea.com/vessels/hokulea/

An archaeological find of a canoe last used about AD1400: Dilys A. Johns, Geoffrey J. Irwin, and Yun K. Sung, "An early sophisticated East Polynesian voyaging canoe discovered on New Zealand's coast", PNAS 111(41), 14728-14733 (2014). https://doi.org/10.1073/pnas.1408491111

For comparison, a replica of Columbus's Niña: http://www.thenina.com/

Partly the answer comes in rephrasing the problem.

Consider Robert Ballard, who made his name in deep ocean exploration, discovering long lost wrecks at incredible depths. This is a very hard problem, the ocean bottom is vast, and wrecks are small, that's a huge search space. But Ballard figured out a smarter way to do it, you don't rely exclusively on just happening to be able to look directly at the wreck itself as the primary way of finding it, instead you track the wreck and make your way to it. And you do this by looking for a debris trail first, which is much larger in area than the wreck itself. Then you follow the debris trail to the wreck.

This is how you min/max traveling between Polynesian island chains in the Pacific. The goal is not to sail from point to point so that you come right into a target harbor on your target island perfectly, that's not necessary. All you need to do is be able to get close enough to any island within a target island chain that you can find your way to that island. Individual islands can be small, and low islands without huge mountains might be visible only from a handful of miles away (due to the curvature of the Earth), but islands cast big "shadows" on their environment. Islands harbor cloud systems at high altitudes which are visible much farther off. Islands act to refract sea swells and ocean currents in ways that are noticeable if you know what to look for. These effects make it possible to detect islands from up to about 30 miles away. That dramatically changes the navigational problem from one of traveling the whole open ocean to find, say, a single tiny, flat 5 mile long atoll (which you'd need to be nearly on top of to see) to instead pointing in a specific direction and expecting to run across a line of current disruptions and cloud formations which form a "wall" hundreds of miles across and 30 miles thick. When you detect that you are within an island block then you can look at the water, look at the clouds, look at birds, etc. to find directions toward land. And once you have made landfall at any island it's comparatively easier to navigate between islands. Even if you "get lost" you can just go back to where you were, the whole island "block" is a huge area and easy to stay within, so you can iteratively problem solve your way toward finding specific islands.

This also helps explain the exploration aspect as well. In some cases it was possible to guess at the existence of other island chains and go exploring. Many of the island chains of south Polynesia are close together, basically neighbors of one another, many of them would inevitably be discovered by accident (through, say, venturing out for fishing) even without concerted exploration endeavors. However, the navigation aspects I mentioned above also make it much easier to speculatively explore other areas for islands, not just because it made it easier to detect being near other islands, but also because it made it much easier to get back. If I leave my island chain to go adventuring but find nothing, I am still fairly sure of my ability to return safely because it's simply a matter of sailing in the right direction and being able to run into somewhere within the huge area of my home island block.

As for the details of long range ocean travel, it's important here to not be fooled into thinking that the only vessels available to the Polynesians were small "canoes". Some of the ocean going vessels of the Polynesians were enormous vessels with the ability to carry many dozens of crew and enclosed structures (houses) built on the deck. These were perfectly suitable for long ocean crossings. Today a reproduction vessel, the Hokule'a, sails all across the Pacific, and it is small compared to some of the largest known Polynesian vessels. Additionally, here again it's important to recontextualize the problem space. It is not necessary to have the capability to travel from anywhere in Polynesia to anywhere else at any time desired, instead the "minimum viable solution" is simply being able to make a voyage with a reasonable probability of success when the time and conditions (ocean currents, prevailing winds, etc.) are ripe for it. And that turns out to bring a lot of the ocean crossings between South Pacific islands into the realm of possibility.

This isn't to downplay the risks of such exploration or to diminish the courage and audacity of the Polynesian voyagers, it took tremendous effort, considerable skill, and enormous boldness to explore and settle the islands of the Pacific. However, it was not a matter of blind "russian roulette" nor of relying on luck carrying the day amidst an onslaught of attempts, as I mentioned, it was a matter of careful skill and preparation as well as boldness and determination.

To learn more on this I'd highly suggest reading the book "Vaka Moana" edited by K.R. Howe, it delves thoroughly into every aspect of Polynesian settlement and history.

This is a good video on how they did it. https://youtu.be/m8bDCaPhOek