Sanderson blundered with this one, it's as simple as that. From his answer so far, he doesn't seem to understand where he blundered, more than it sounds as if he's trying to cover up a mistake he's aware of.

The first Perrin chapters in TGS had a few continuity errors. It seems to have been written at the last minute, to provide Perrin material for the first book. It seems to have been created from the ground up by Sanderson, as some sort of "prequel", likely because Perrin's storyline started too strongly to his taste, and was hard to split. So he wrote a few chapters full of nothing taking place before the first AMOL chapter RJ planned for Perrin (it's sort of obvious RJ intended to jump to the Jehannah Road, and the disappearance of Gill and co. right away - the intro chapters were the death of Masema and the Perrin dream scene in the prologue).

In TGS Brandon had Perrin still had Malden when it's Tylee who remained behind to deal with the Shaido. Perrin had left right away. The pressing issue of food to feed so many new mouths was largely overlooked - Faile had seized Sevanna's jewels precisely for that, but nothing was made of that in TOM.

The other mistake came about with that silly, and useless conversation about Balwer's calculations re: gateways. The issue wasn't the number of refugees and how long the gateways would have to remain open, it was, as established in KOD, that Grady and Neald had pushed themselves to the point of channelling exhaustion and would give all they had left at Malden. Clearly, RJ planned to have them incapable of channelling much at all for many days after, if not longer. Jordan had taken care of the issue of tied-off gateways in KOD.. Sanderson's wrong. Grady and Neald know about tied-off gateways to spare their stamina. RJ established that this wasn't part of their habits, they started doing that too late to avoid exhaustion. Perrin knows about this. It's Perrin, right before Malden, who comments to himself in KOD that Grady had not much left in him and that he's begun to tie-off his gateways to spare what he has left. Perrin also comments it's a pity it's too dangerous to leave that gateway (the one to the TR to fetch Tam and co.) open during the battle, as he would very much have liked to send Faile and the others to the TR right after the rescue. The implication is clear: Perrin was already aware before the battle that the Asha'man would not be able to provide him gateways afterward. His plans also took this into account, he had sent the serving staff ahead to the Jehannah road and intended to follow...

The whole scene about this in TGS makes no sense. Not only Perrin knew about this issue already and it shouldn't have been news to him (some even theorized that the whole thing was so weird that it made Balwer suspicious.. so much for that!), but if you present the problem as Brandon did, Perrin also knew the solution: tie-off the gateways.

It's very clear RJ intended the Asha'man with Perrin to be out of commission for a while as AMOL began - it's all there in KOD. That long-term exhaustion makes sense considering what we know of channelling (and the relative inexperience of these two), and it had been long established that the Asha'man during the 60 days of hunting for Faile had gotten so fatigued that they slept whenever they were not needed. RJ never provided an explanation as to why Grady and Neald didn't start to tie-off their gateways before the eve of Malden, but it's probably inexperience (IMO, they didn't fully realized before it was too late the sort of exhaustion they were facing if they kept going at that regime... but honestly Masuri and the other, or the WO, could have told them to slow down...).

In any case, it's where Sanderson blundered. How long it would take, holding gateways open, to send off each refugee group away had nothing to do with the reason why Perrin couldn't send them away. The issue was that Grady and Neald were both suffering from channelling exhaustion and needed to recuperate for a long time before they could channel normally again. Even if they started slowly when they began to recuperate, likely they would not have been able to open many big gateways a day. The refugees were from all over the place, it would have taken forever to send all the groups away if the Asha'man could only make a few tied-off gateways a day,

There was also the issue that if they gave all they had for gateways, they would be useless in case of trouble, leaving only the WO - and the two AS bound by the three Oaths. With so many refugees on foot in the wilderness, with bad sanitation, poor clothing and with very low food stocks, Healing among other things should have taken much of the women's channelling each day. It wasn't really was to use the Asha'man up for gateways, to send away such a small percentage of people. In case of emergency, that would have put over 100,000 people at risk.

Sanderson totally overlooked the fact Grady and Neald knew how to tie-off their gateways and Perrin was aware of it, and he added unnecessary details that turned into continuity errors.

He didn't change the ruled to fit his plot, he simply overlooked how RJ had already covered this issue in KOD.