How could a White Russian victory be achieved?
for starters land reform could've been taken up much earlier as a counter to the Bolsheviks' land reform program in the countryside, which was indeed taken up by the Whites but only after Wrangel came to lead the Whites after Denkin's resignation which was rather late by that time.
Furthermore, a right-wing military coup could very well occur in Petrograd sometime in 1918. The British agent Captain Cromie was actively involved in fomenting counterrevolution in Petrograd, but was killed before he could continue his work to undermine the Soviet government.
Petrograd at that time was dealing with dissent primarily from workers whose support had originally been critical for the October Revolution, the Red Guard having been a major source of strength for the Military Revolutionary Committee (MRC) which spearheaded the insurrection in October.
Also, the Bolsheviks had by 1918 also managed to antagonize sailors too.
So by 1918 there were a lot of factors going against the Bolsheviks and in favor of the Whites/counterrevolution.
1918 IMHO is the earliest date for a White victory in the civil war, most likely spearheaded by Cromie and Co., whom would most likely set up a rightist military dictatorship or a possible (but rather unlikely) restored monarchy.
Which is a big if. IMHO the Whites didn't stand a chance in 1919, 1920, or beyond.
The thing was, the Whites were not only top-heavy with officers but in the minds of the people they embodied the counterrevolution (Kornilov being a prominent White leader before his death, Kornilov having led an aborted coup in 1917 prior to the October Revolution)
Wrangel had gotten the idea for land reform by 1920, but by then the White movement was looking increasingly weak.
The Bolsheviks won because they were at least willing to carry out radical policies in the cities and in the countryside. The Bolsheviks had already beaten Wrangel to the punch long before 1920 with their 1917 decree on land.
they could restore the Tsar, or maybe set up a republic
The Whites wouldn't necessarily restore Nicholas II to the throne, and by 1918 the Romanov family would be no more. (killed for fear that the advancing Whites would turn them into a living symbol of the counterrevolution).
At the very least if monarchy is restored one of the Romanov's relatives could take the throne and rule.
As for a republic, it depends. Kolchak had essentially made himself supreme ruler by 1918 in territories under his control.
Furthermore, the relationship of the military to the republic could very well be shaky, if barely functional at best.
Again, IMHO, 1918 stands as the most likely year for a White triumph in the form of a military coup in Petrograd.
This would liquidate "soviet power" in Petrograd and allow for the Whites to assume power in Russia without having to beat the Bolsheviks in the field, something which they proved surprisingly inept at throughout the civil war.
I don't see a restored monarchy as impossible, but unlikely due to how the Romanov family was viewed in Russian society by 1917, let alone 1918. But it's not impossible, a restored monarchy something which Cromie and his co-conspirators seriously considered in 1918.
Like with China and it's revolution and civil war, a successful counterrevolution (called "a change of sky" in China) would and could lead to the supremacy of the conservatives which formed the bulk of the White movement.
Bolshevism, soviet power, etc. would be stamped out as the conservative leaders of the White movement find themselves having to increasingly rule through the use of the bayonet.
Fascism could very well arise in Russia then, either through a restored monarchy (as in Harry Turtledove's TL-191 series) or through the military which would effectively have put Petrograd and other cities in Russia under martial law for some time after the defeat of the Bolsheviks.
The White regime would most likely be right-wing and highly conservative, with a strong streak of authoritarianism and with an emphasis on the military which could very well hold immense power in this alternate Russia.