Ok' I ve been at this for several hours today and have tried several different strategies for this mission so I thought I'd share what I have learned.
First of all, I've not even once managed to win the battle of attrition some posters here say they've been successful at, and I've tried this at least 10 times, using different henchies, different skillsets and picking different spots to do the battle. Now it's possible that I simply suck at this, however one thing I can say for sure is that the White Mantle never even once came "one by one". Normally, a second group of four is close on the heels of the first one, and while it's easy to dispose of the crystal carriers, it was impossible for me to kill them all before yet more of them started to arrive (with no crystals this time - they're coming to fight). And usually when the next crystal runners appeared, I was still fighting 4+ mobs, and then their escorts joined in and either one of the runners got through or my party simply got overwhelmed.
On the other hand, the running strategy suggested by JediNeophyte (2nd post in this thread) worked wery well for me. I have only a fairly weak run buff at my disposal (at least I thik so - 25% for 12 seconds, with ~30 sec refresh?) but was able to gain advantage relatively quickly, and within about 4 or 5 minutes all the pedestals were mine. The only trick to this is to keep on running... In my experience, taking the pedestal closest to the guardian at the begining didn't make any difference, tough it caused me to cross paths with the Mantle runners, while when not taking it I completed the mission without running into them at all.
As some other posters have mentioned, having a better run buff should actually make this quite easy.
There's actually an interesting twist to this strategy if you want to complete the bonus as well (or do the battle for for any other reason). I'll get to this in a sec.
A point I'd like to stress is, I am not saying that it's impossible to win the battle. I was twice able to hold out for quite long, killing 5-6 crystal carriers (and probably 10 or so other mantle) before one got through - and it's also important to note that my character is hardly optimized for damage dealing (lvl 20 healing Mo/R, i usually keep at least 10 points in marksmaship, but obviously am unable to spam special attacks the way primary rangers can, also and my bow is a bit subpar as I am a newb - no elite skills, either etc. etc.). So having an 'ubar' character with better skills/equipment, and also being a better player

might make enough of a difference in killing time to make it possible to win this one.
A few other points I believe important:
- configure your character for maximum possible damage output, as it's (quite obviously) crucial to be able to kill the Mantle as quickly as possible
- if you have healing capabilities, don't equip healing *enchantments* such as Healing Breeze or Vigorous Spirit, as they are likely to fail you at the crucial moment. (White Mantle Ritualists like to use Well of the Profane skill which renders these enchantments useless, however, regular healing spells work normally)
- other than crystal carriers, Abbots (healers) and Savants (elems) are the primary targets (Savants' Searing Heat can easily do way too much damage to your party for Alesia to keep up with, especially when you're fighting several of them)
- in my experience, pinning down didn't (obviously

) make enough of a difference but nonetheles can be very handy when a Mantle runner threatens to get past you and ruin the mission for you (alas, it has a very high energy cost for a secondary ranger with no Expertise, who is also a healer

)
- and finally, the running strategy can be used to weaken the enemy before the battle. The trick is to make sure you cross paths with the White Mantle runners and maybe even stop for a second or two so that your henchies engage, and then you KEEP ON RUNNING. They'll follow you for a bit and exchange some blows with the henchmen, however, they end up scattered and isolated on the map (after they've engaged, they never return to the Mantle camp) so that once you are comfortably ahead in the pedestal race you can stop for a few sec and easily pick them off, one by one. I am not sure for how long this strategy can be continued (IMHO it's possible that killing the second runner, or other somesuch event triggers the outpour of White Mantle from the camp). I didn't have the patience to continue this for more than a few mins, but if it works, it might actualy make the forthcoming battle much more winnable.
DOH, I just realized that this is more or less what Neophyte Jedi was talking about in his post, so it should definitely work I am not editing this out though, it took to much typing hehe.
On a final note, that Demagogue guy must be a quite a turd and certainly not a 'champion' of any kind, because with the advantage he holds he should be winning the mission 100% of the time, hands down [just kidding, obviously]