MFIs don't post listings to "Kiva.org," they just upload them through their "back door site." Kiva staffers decide what gets posted for us to see and when (not counting those sneaky peekers).

If there truly is a backlog of loans uploaded through their "back door", then I think it would be pretty simple to scramble the new loans actually posted.
But I suspect the reason we get chunks from one MFI and then chunks from another is there isn't much reserve available to choose from, internal constraints having been imposed.
Again, it wouldn't be as much of an issue if we had closer to 100 loans posted on the website. Then six to ten from the same MFI at once would blend in much easier.
(And I will again grudgingly admit that the default sort by "popularity" does increase the dispersion of the "chunk".)
Dan