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OK, having implemented that design matrix, the problem I'm getting is that it's rank deficient, on the order of 1E-17 (i.e. well past the recommended tolerance of 1E-4). Here's the matrix again, just for reference, with two subjects (one in each group):

Grp TRPR TRPO SHPR SHPO S1 S2
1 1 0 0 0 1 0
1 0 1 0 0 1 0
2 0 0 1 0 0 1
2 0 0 0 1 0 1

With contrast:

Con	TPR	TPO	SPR	SPO
Ixn	-1	1	1	-1

... or (TPO-TPR)-(SPO-SPR).

In the actual design matrix, there are 22 subject EVs and multiple subjects per group. A TIFF of the full design matrix is attached, in case it's of interest. I believe the issue is in the first four EVs (call them the "experimental" EVs, since they represent conditions and not subjects). Going by the FEAT examples at http://www.fmrib.ox.ac.uk/fsl/feat5/detail.html, it looks like one easy way to deal with this is have the experimental EVs code factors rather than levels, and change the contrasts a bit:

Grp TT ST S1 S2
1 -1  0 1 0
1  1  0 1 0
2  0 -1 0 1
2  0  1 0 1

(where "TT" means "truly stimulated, time factor" and "ST" likewise for sham.)

With contrast:

CON	TT	ST
Ixn	1	-1

... and then I should be able to get the overall effect of time with:

CON	TT	ST
Time	1	1

... and the simple effects of time with:

CON	TT	ST
True	1	0
Stim 0	1

(I mention these latter things less because I'm interested in them and more as opportunities to betray any flaws in my reasoning... as if I needed more opportunities.)

I'm semi-confident about this, but if anyone has the time and inclination to check my logic, I'd be grateful. Thanks! (And thanks again to Donald for getting me this far.)