Given the general composition of plastomes (coding regions with triplett structure, tRNA and rRNA genes, non-coding regions, I wonder if a distance-based tree (how were the distances calculated?) provides branch lengths that allow proper comparison between the main clades.

Maybe you can use the matrix you used to infer pairwise distances for a quick, partitioned ML analysis (e.g. with ExaML: https://github.com/stamatak/ExaML)? E.g. one partition for 1st and 2nd codon positions, one for 3rd (given the distance between Fagus and other Fagaceae, this position may already be saturated), one for structurally-informative genes (tRNA genes, rRNA genes), and one for all non-coding intergenic "junk".

For orientation (of Fagaceae-interested readers), you could also annotate the oaks section names for the oaks you included in the tree. Q. glauca: section Cyclobalanopsis (subgenus Cerris) Q. variabilis: section Cerris (subgenus Cerris) Q. aliena: section Quercus (subgenus Quercus) Q. aquifolioides: section Ilex (subgenus Cerris) [Q. rubra, complete plastome available in gene banks, would be section Lobatae (subgenus Quercus)]