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<batch> is perfectly appropriate for that purpose. Set up three <batch> elements in a file:

<batch>
/ file  = "IAT_A.iqx"
/ subjects = (1 of 3)
/ groupassignment = groupnumber
</batch>

<batch>
/ file  = "IAT_B.iqx"
/ subjects = (2 of 3)
/ groupassignment = groupnumber
</batch>

<batch>
/ file  = "IAT_C.iqx"
/ subjects = (3 of 3)
/ groupassignment = groupnumber
</batch>

(In the three IAT scripts themselves, you'll probably want to change the /groupassignment in the <expt> elements to either subjectnumber or random.)

You register the file containing those <batch> elements as you active web script. You upload the IAT scripts and associated files (if any) in the next step. Set the launch page up to retrieve the group id from a URL query parameter via the web script wizard. Let's call this parameter 'IAT' for the sake of example.

Then you simply give your participants a different link for each week. For example, for participant X you might give her/her

Week 1: http://research.millisecond.com/yourusername/iatbatch.web?IAT=2
Week 2: http://research.millisecond.com/yourusername/iatbatch.web?IAT=1
Week 3: http://research.millisecond.com/yourusername/iatbatch.web?IAT=3

which means s/he'll complete IAT_B in the 1st week, IAT_A in the 2nd week and IAT_C in the 3rd.

You might give participant Y

Week 1: http://research.millisecond.com/yourusername/iatbatch.web?IAT=3
Week 2: http://research.millisecond.com/yourusername/iatbatch.web?IAT=2
Week 3: http://research.millisecond.com/yourusername/iatbatch.web?IAT=1

which means s/he'll complete IAT_C in the 1st week, IAT_B in the 2nd week and IAT_A in the 3rd, and so forth.

That way you (a) have full control over the assignment of IATs (if subjects are allowed to select the IAT to complete themselves, they might mistakenly complete the same IAT several times) and (b) don't have to delve into any complex branching or the like at all.

Hope this helps.

That sounds great, will give it a go. Thanks very much for all the detail.