Is it ok to interprete PCA plot this way?
Given the information provided, I do not think it's enough to say that your samples are between stages D12 and D19. I admit knowing nothing about your domain, but with what you're showing it is very conceivable that other factors are causing the spread of your samples from the others on PC1 and it's too much of a stretch to say that your samples "project" into the others in between D12 and D19. Why does it have to be a projection orthogonal to the axis described by PC1? Remeber that PC1 is a linear combination of all your inputs. That is, it describes an arbitrary line through your input space that is probably not aligned with any one thing in particular. For example, all three of the following projections could be envisioned for your problem:


Another red flag for me is that you say PC1 is related to differences in experimental protocols. You haven't posted a scree plot or listed the eigenvalues for the different PCs but obviously PC1 soaks up the most variance so it's a pretty big deal. If you're saying that PC1 is correlated with experimental protocol, then that would seem good because hopefully the impact of experimental protocol is minimized in other PCs. However, that's never completely the case, really.

Again, not knowing your domain it's hard to tell what the impact of experimental protocol is on the distribution of your data in the PC plot, but I'd be VERY wary of comparing these data in this way if your data was produced using a different experimental design and, as you noted, "there may be other differences." 

My hunch is that you would need to continue minimizing differences in the protocols between your experiments and the published experiments before you could really use this type of analysis. Others might disagree but if you posted the sources of your data, the eigenvectors, and possibly a subset of the data, experts in your field may be able to chime in on this methodology. 

The short answer is: you could be right in your interpretation but at this point you don't have enough evidence to suggest your samples are "in between" D12 and D19 in terms of the stage. And I worry about differences in methodology completely swamping your ability to interpret things this way.