I don't believe there's faster domain back order companies.
What you should think of is when the redemption period is over who will know it first? Of course the current registrar. So if you want to know where to pay for back ordering a domain, the answer is pretty simple:
go with the domain's current registrar if you can, you'll have much more chances there.
Try to wait the longer before backordering, so the domain won't get transfered somewhere else.
Most registrars are renewing domain names 30 days before it expires so the best time to back order, in my opinion, is within those 30 last days.