DOE blocking and a confounding factor

[#1]

Ok. So, I have an experiment with 5 (five) 2-level factors, F1, F2...F5. An additional variable, not of direct interest, was a hard-to-change factor that called for a  (blocking) variable F6 that essentially divided the experiment into 2 separate 1-week blocks. That's because one of our participant groups had to divide their participation into one week or the other, and we wanted to block for that effect. Let's call the levels of the blocking variable as participant group A and participant group B.  

I had a run budget of 32 runs. So I had two blocks of 16. I was interested in main effects and 2-way interactions for the five main factors of interest F1-F5. 

At some point, someone introduced another complication: in addition to the blocking factor (participant group), I learned there were 2 individuals within each of those participant groups A and B; rather than each run being associated with a specified participant group A or B, as intended, each run was associated with one specific individual within their respective group — that is, one of those two individuals was assigned specific runs within their respective 16-run blocks. That is, individuals 1 and 2 executed (alternately) runs within block 1, and individuals 3 or 4 executed runs (alternately) runs within block 2.  

If I ignore those individuals, and simply treat the design as if it was a randomized design with two blocks, where the blocks are defined by their participant group, what am I doing to my analysis? I assume there will be 'unseen' variance stemming from the fact that there are two individuals within those participant groups, affecting each run differently. Is there a way that I should be conducting or caveating the analysis (ANOVA), knowing how the experiment was actually conducted?

[#2]

You have options...which one is the best we probably won't know until after you get some data.  My thoughts:

What noise are you confounding with the block?  I see you mention weeks, but what (noise) is changing in that time period that you want to separate from the treatment effects?  What are the hypotheses associated with blocks and in particular, participants?  Can the participant variation be studied using sampling rather than experimentation?  This way you also get some idea of the participant consistency.

You have several  options (each option will require a different model for ANOVA).

1. Treat the block as a random effect and the participants randomized within the blocks.  The participants would not be assignable, and their variation would be allocated to the block effect.  With this, you could still keep track of the 4 participants and look for systematic effects using graphical analysis.

2. Treat the block effect as fixed and choose just 2 of the 4 participants based on hypotheses as to why they would impact the response variables (e.g., experience level).  Confound one of the participants with the first block and the second with the second block.  This would allow estimation of the block effect and block-by-factor interactions.

3. Add the participants as an incomplete block and replicate this in 2 complete blocks.  Obviously you'll give up some resolution with this approach, but it would still be a reasonable res. IV design.