I propose to base your naming on a linear synteny plot, e.g. using syntenyPlotterR. Your question implies that the ancestral chromosome organization could be a relevant criterion to resolve the naming, say if we reconstruct the chromosome structure of the common ancestor, e.g. using DESCHRAMBLER, and name them simply Chr1... ChrN, you could name all highly conserved chromosomes the same way. For mosaic chromosomes or rearrangements, you could use a naming scheme that reflects their components. For 11 samples, you could likely do this manually based on the synteny plot. This method works with pairwise alignments and should be computationally feasible.

The plotting is the part that won't scale, and I don't think you actually need it. You already have the all-vs-all alignments - turn each pairwise alignment into one number rather than a picture and you've got a 48x48 matrix you can just cluster.

From the PAF, something like bases of A covered by alignments to B divided by length of A, made symmetric by averaging both directions. Then 1 minus that as a distance, hierarchical clustering, cut the tree, each cluster becomes chrA / chrB / chrC. That's a short pandas + scipy script over files you've already generated, and the grouping ends up reproducible instead of eyeballed.

The k-mer suggestion was also better than it sounded - Mash and sourmash aren't metagenomics-specific, they're general genome distance tools, and mash triangle hands you that same matrix directly in seconds. Two things to watch there: with chromosomes of very different lengths Jaccard distance is biased against the short ones, so sourmash containment behaves better; and given your repeat content I'd mask repeats first either way, or unrelated ACs will look similar purely through shared TEs.