Fantastic, I have been following the "Multilevel Experiments" section (pg 51) and it more or less makes sense but I am not sure about the  duplicateCorrelation part.  The difference between my experiment and the example is that each of my subjects is exposed to all conditions, while in the example, some subjects have diseased tissues and others have normal (rather than all subjects having both diseased and normal). 

I went through, following the example like so: 

#In my exp, Treatment is analogous
#to "condition" in the example, Time is analogous to Tissue
# and TissueID is to subject.

#combine the Treatment and Time parameters into one
Treat <-factor(paste(targets$Treatment,targets$Time, sep="."))

design<-model.matrix (~0 + Treat)

#Then we estimate the correlation between
#measurements made on the same subject

corfit<- duplicateCorrelation(expressedProbes.lumi,design,
                              block=targets$TissueID)

corfit$consensus
#[1] 0.03368044
#I guess this means the TissueIDs are not significantly correlated?

#Then this inter-subject correlation is
#input into the linear model fit

fit <- lmFit(expressedProbes.lumi,design,block=targets$TissueID,
             correlation=corfit$consensus)
#Now we can make any comparisons
#between the experimental conditions
cm<-makeContrasts(
  SD90.3vsMock.3 = TreatA.3-TreatMock.3,
  V186.3vsMock.3 = TreatB.3-TreatMock.3,
  levels = design
)

fit2<-contrasts.fit(fit,cm)

fit2 <-eBayes(fit2)

topTable(fit2,coef="TreatA.3vsMock.3")

 But, the final paragraph of the section on pg 52 mentions that

"Here the comparison between tissues can be made within subjects [true for my experiment], and hence should be more precise than the comparison between diseased and normal, which must be made between subjects [not necessarily true for my experiment, since all subjects have all treatments]."

So maybe I need to do something different?

However, even though I can do all my comparisons within subjects, I still want to be able to say something about differences in gene expression between the different treatments in general, not just about these particular tissue donors. If my googling of the definition of random effects has given me the right answer, it seems more right to keep the analysis as is.