Reward and Punishment
The whole period of Rosh Hashana, Yom Kippur and even Succot through Hashana Rabba, is a period of judgment. The righteous are judged for life, the wicked for death, and the rest are in balance depending on how they, or G-d, decides to tip the scales.
This judgment is for life in this world, including all its material facets like health, wealth, tranquility, etc. And, in fact, the Torah itself repeatedly states that those who do G-d's bidding will receive blessing in this worldly-terms; while those who don't will suffer.
My question is: the Talmud and classical commentators explain that the righteous are rewarded in the next world, while it's the wicked that are rewarded for their few good deeds in this world. The result of this is that in this world, the righteous tend to suffer while the wicked tend to prosper. How can these seemingly contradictory ideas be reconciled?
This is a very good question, and one which the Torah commentators raise in several places.
It is true that regarding observing the Torah in general, and throughout this period of judgment of the High Holidays in particular, we are promised that the righteous will be rewarded. And as you point out, this reward is described in this-worldly terms.
Yet, we are taught by the Sages that "the reward for mitzvot is not in this world". Rather, it will be in the World-to-Come. This is one of the reasons behind the idea you mention that the righteous will be rewarded for their good deeds in the World-to-Come, whereas their few misdeeds will be "rewarded" in this world in the form of suffering, in order that they reap the full benefit of their righteousness in the next world.
However, if this is true, although we can understand why the wicked will be punished in the next world for their misdeeds, why are they rewarded for their few good deeds in this world? According to the teaching of the Sages quoted above, there's no reward for mitzvot in this world!
The answer to this question also answers yours.
In addition to teaching us that the reward for mitzvot is not in this world, the Sages also teach us that while the "principal" accrued by the mitzvot is rewarded in the next world, the "interest" on that principal is paid out in this world.
Therefore, the fact that the principal will be retained for the righteous in the next world doesn't mean they'll necessarily suffer in this world. It’s the "interest" on their investment that the Torah promises as blessing for doing G-d's Will, or as life and its bounties conferred upon the righteous during the period of judgment of the High Holidays.
On the other hand, the reward given to the wicked in this world for their few good deeds is actually the principal itself. Even though the reward for mitzvot is not in this world, that's specifically in the normal state of affairs. However, the wicked, by investing their efforts in the physical world, make it the place where their principal is paid. This results in their reaping the full "reward" for their misdeeds in the World-to-Come.
So to summarize, the "this-worldy" blessing promised to the righteous is paid from the interest on their holdings in the World-to-Come. And even though their few misdeeds are simultaneously reckoned here as suffering, that's only to preserve the integrity of their investments there. Whereas the wicked receive the full reward for their good deeds here, and suffer the full repercussions of their wickedness in the World-to-Come.
In what way, then, is the Torah's "this-worldly curse" against wicked realized?
For one, even though they may have bounty, they don't have blessing in that bounty. They are never satisfied with what they have, they're constantly driven by jealousy and competition to have more, and therefore don't really enjoy what they have. The righteous, however, in spirit with the teaching of our Sages, "Who is wealthy? He who is content with his portion", are grateful for and happy with G-d's gift - which is blessing. And this is a further curse for the wicked, who — seeing the righteous content with less — seethe with dissatisfaction and dismay.