Hi Michael!
I’ll do my best, but I’m not an expert SPM user. I do know what the design matrix should look like and am great with FSL!
I feel approaches 1 and 3 should be the same. Your results look roughly the same and some differences might occur because model 3 assumes the tasks are independent, but they might actually be correlated (meaning the level 1 regressors are correlated). Also, the residual variances will differ between the two models. At least from what I’m seeing here and based on what I know about SPM, I think they should be very similar.
Approach 2 is wrong. From what I can tell you’re not adjusting for repeated measures.
I think I answered the 2nd problem, correct?
Of course this doesn’t test your interaction. You didn’t ask, but I’ll tell you how 
I’m going to use V1T1, V1T2, V2T1, V2T2, V3T1, V3T2 to describe your 3 conditions. Your F-test of interest is
V1T1-V1T2=V2T1-V2T2=V3T1-V3T2
to get the contrasts for SPM, do some algebra to get a 0 on the end. I’ll subtract V3T1-V3T2
V1T1-V1T2-V3T1+V3T2=V2T1-V2T2-V3T1+V3T2 = 0
So the two contrasts you’d specify and then select for your F-test for the interaction would be
V1T1-V1T2-V3T1+V3T2
and
V2T1-V2T2-V3T1+V3T2
Then if you find a significant interaction you can use either this same model or the first option to test what’s driving the interaction.
Hopefully that covers problems 1 and 2!
It is possible to run a group analysis in FSL without feat directories and it uses flameo. More here
http://blogs.warwick.ac.uk/nichols/entry/flame_without_1st/
I don’t know how to incorporate that into NiPype.
Hope that’s helpful.
Cheers,
Jeanette