Found a solution and calculated a reduced model of the ANOVA excluding the unallowed effects.

Yes. You can enter the data, and run the analysis. What you get out may not be helpful. If you have 20 observations and the answer is always 42, then the standard deviation is zero. If this is the dependent variable then no independent variables will be significant. If this is an independent variable it will have no effect on the dependent variable. The statistics program will print blanks, missing values, or give some other indication that the model has failed. So what is the point of including a constant in the model?

There is another option. This may be telling you that you have insufficient replication.

In the "think outside of the box" context you could have a synergist/antagonist. Compound A has no effect on its own, and never will. It has an effect on the performance of factors B and E, but it does so at such low concentrations that there is no dilution effect. As such you expect that the main effect of A is zero, and there will be two or more interaction effects. I say "or more" as I have no idea if the ABE interaction effect will be significant. It is kind of odd that all 20 replicates had a value of 42, because one might guess that measurement error alone would introduce some variability.

Even if your research question is about the interactions, you should still care about the main effects. If nothing else they help other researcher's decide if your research is worth anything. If the standard paradigm states that the effect of C is 12.7 (SD=2)and you show that it is 12.6 (SD=2.04) people will probably want you to move on quickly. However, if your value of C is -4.7 (SD=1.09) then you have some explaining to do.

Yes. Required.