I've been re-reading the WoT series, and I saw this question a while ago. So now that I've gotten to AMoL, I've been able to take note of some details to help answer this question. That being said feel free to comment if I've missed anything or if you think some of my estimates are wrong.
edit: added notes about Turning, as the OP was asking very specifically about that
Note that this answer contains some spoilers.
Groups of Channelers during the Last Battle:
On the side of the Light:
- White Tower
- Wise Ones (but not the Shaido, except for those who were captured as damane)
- Black Tower
- The Dragon Reborn
- The Kin
On the side of the Dark One:
- The Forsaken (Demandred, Hessaslam, Cyndane, Moghedien, Moridin, M'Hael)
- The Ayyad (Sharan channelers)
- Asha'man (Taim's cronys + Turned Asha'man)
- Black Ajah + Turned Aes Sedai
- Samma N'Sei, the male Aiel channelers
- The White Tower contains roughly 1000 Aes Sedai. Some of these are Black Ajah and some are captured during the Seanchan raid.
- Taim is given a goal of finding 1000 male channelers to balance the White Tower. I don't have a reference, but I imagine he got to his goal.
- The Shaido Wise Ones contain 400 channelers. If we accept the wiki estimate, there are then around 4400 channeling Wise Ones in the other eleven clans. This estimate seems to me to be quite large, but it is certainly an estimate. It's not unreasonable to expect, provided that the Samma N'Sei were given protection from the taint, that they are an equal number to the Wise Ones, if we assume that male and female channelers are evenly distributed among the Aiel. Even if there are fewer Samma N'Sei, a good number of the Wise Ones are very weak in the power, so the forces at Shayol Ghul are probably close to parity, strength-wise, if not in numbers.
- The Kin number around 2000 (1783 to be exact). Most of these are likely restricted to healing duty in Mayene, though perhaps some were used for Traveling. IIRC their pact with Elayne also allows them to decline fighting in Andor's wars, so it's unlikely that they take part in the battle apart from Channeling/Healing.
- The Windfinders seem to only be channeling around Shayol Ghul with the Bowl of the Winds, so I think we can safely exclude them from the battle count.
- There are ~200 Black Ajah, as recorded in Verin's notes. 50 of these are executed by the White Tower, the rest of whom escape.
- A quote by Demandred provides some insight while speaking with Taim:
[...] consider this: You may have a hundred pet Asha'man. I have over four hundred of my Ayyad.
Any estimate for number of damane is extremely difficult to pin down. Fortuona is quite excited at the prospect of leashing the Aes Sedai:
"Fortuona could swoop in and all of those damane would be hers. Hundred upon hundreds. With that force, she could crush the resistance to her rule back in Seanchan." (A Memory of Light, Chapter 24)
These "hundreds" of channelers represent the remaining Aes Sedai left on the battlefield, not the Sharans (I think. Note that the Seanchan are aware that the Aes Sedai are useless as weapons so perhaps they are referring to the Sharans after all). Several hundred channelers would, in addition to the Imperial damane, be sufficient to destroy all forces in Seanchan, so I would hazard a guess that the Seanchan have roughly 400 damane of their own as part of the Corenne, in addition to any new ones captured, such as the Shaido Wise Ones. Some of them are surely left in Seanchan-held territory, as the Seanchan would want everything to be in order. My best estimate is that they bring in maybe 600 channelers of their own.
Tallying it all up
500 Aes Sedai
4000 Wise Ones (all at Shayol Ghul)
0 Windfinders (none who actually battle, anyway)
All for around 5100 channelers.
200 Turned / Black Ajah Aes Sedai
100 Turned / Darkfriend Asha'man
4000 Samma N'Sei, all at Shayol Ghul
for around 4700 channelers.
So it would seem that the numbers are much closer than you think.
- The Forsaken. Having 4 of the most powerful channelers in history (3 if you don't count Cyndane, who seems to be doing her own thing) gives the Dreadlords a sizeable advantage, both in terms of raw strength and knowledge -- using sufficiently powerful balefire might revive Shadowspawn/Sharans that were just killed, and they're using it relentlessly.
- The Sharans show up once the Aes Sedai / Asha'man are tired out, having expended their strength holding back the Shadowspawn armies. Demandred even shows up with a full circle of seventy-two, holding the Scepter and annihilating quite a large number of the Aes Sedai/Asha'man.
- The ability of the Sharans to link (which the damane cannot) also gives them some advantage over the Seanchan, even if the damane are in greater numbers than I suggest.
- Nearly all the full Asha'man, the strongest in the Black Tower, are either Taim's cronies or Turned, so they would in theory each be stronger than the Asha'man on the side of the Light.
A few notes about Turning
added at OP's request as Turning was the main focus of the question
Although Taim had 100 Asha'man on his side, it seems that the Turning process took a long time and a great deal of effort. With 100, he would have been able to Turn 7 at any given time, provided he had enough Myrdraal, which would have sped up the process--Turning 7 twice would have allowed him to Turn 8 at a time, and so on and so forth. There are a few reasons why it might have taken longer, as it seems to me:
- With that many Myrdraal around, the Aes Sedai outside (and the Asha'man) would have been alerted to the presence of Shadowspawn. This is also a good reason why the Black Ajah didn't just Turn a bunch of Aes Sedai (before they were executed, anyway).
- It's harder to Turn a male channeler with saidin than saidar, at least according to Androl.
- The Black Ajah doesn't show up at the Black Tower until later, once Moridin raises Taim to the Chosen. Together, the Black Ajah and the Asha'man join the battle at Tarwin's Gap--Taim leaves his lackeys to turn Toveine immediately before Dreadlords show up there. Taim surely brings his most powerful (or well-rested) channelers, and less powerful and tired channelers would likely slow down the process.
- Finally, an off-the-wall theory of mine: Maybe male channelers are able to resist Turning better than females, in the same way they were able to resist the Dark One's taint? Just as a matter of practice, not because of any innate qualities.