Hmm yea, I agree that the lymphatic system is the primary route of mRNA vaccines, based on the relevant mRNA vaccine biodistribution studies in animals thus far.

At this point, I've not come across any studies that can definitively answer your question about mRNA vaccine's LNPs crossing endothelial cells and then expressing spike proteins. But at least in theory, LNPs are known to cross endothelial cells of the blood-brain barrier, which makes LNPs great carriers of drugs into the brain. This is one of the basis for the concerns of mRNA vaccine entering the brain.

I think it's inevitable that injection will rupture some capillaries considering that muscle tissues are highly vascularized. After all, there's always a bit of blood after injection. So, yes, I think a tiny amount of LNPs can enter the bloodstream this way. But the consequences of this is most likely inconsequential, as discussed in this article.