Ancestral genome reconstruction is an important task to analyze the evolution of genomes. Recent progress in sequencing ancient DNA led to the publication of so-called paleogenomes and allows the integration of this sequencing data in genome evolution analysis. However, the de novo assembly of ancient genomes is usually fragmented due to DNA degradation over time among others. Integrated phylogenetic assembly addresses the issue of genome fragmentation in the ancient DNA assembly while aiming to improve the reconstruction of all ancient genomes in the phylogeny simultaneously. The fragmented assembly of the ancient genome can be represented as an assembly graph, indicating contradicting ordering information of contigs. In this setting, our approach is to compare the ancient data with extant finished genomes. We generalize a reconstruction approach minimizing the Single-Cut-or-Join rearrangement distance towards multifurcating trees and include edge lengths to improve the reconstruction in practice. This results in a polynomial time algorithm that includes additional ancient DNA data at one node in the tree, resulting in consistent reconstructions of ancestral genomes.