Quantitative phylogenetics in historical linguistics has relied almost entirely on lexical cognate data. This study asks a different question: how much genealogical signal can be recovered from structural features extracted from annotated corpora, and whether it survives at deep time depths. We compute 29 structural features-including Shannon entropies of dependency direction and of dependency-relation distributions, relation-specific directionality ratios, dependency-distance measures, and constructional ratios-across 25 Transeurasian languages from the five proposed groups (Turkic, Mongolic, Tungusic, Japonic, and Koreanic) and three outgroups (Chinese, Vietnamese, and Hindi), 28 languages in all. Most of the Tungusic and Mongolic languages have no running-text corpus, so we built new Universal Dependencies treebanks for them by glossing example sentences from reference grammars; thirteen are used here. Each feature was tested for phylogenetic signal (Pagel's λ and Blomberg's K, with FDR correction) under four competing reference topologies, and the features that passed were used for tree inference (Bayesian inference in MrBayes, with Neighbor-Joining as a check). The same pipeline was first run on Indo-European in a companion study, where it recovers only individual subgroups and does not resolve a stable tree. At the depth proposed for the Transeurasian family (a Proto-Transeurasian root of about 9000 years before present), the structural signal was not enough to reconstruct the family's internal relationships. The signal tests favoured a flat three-way division of the major branches (7 strict/20 relaxed features) over any nested hypothesis (≤2 strict features each), and the strongest signal lay in core word-order parameters (e.g., object direction, λ = 1.00, K = 6.06). But both Bayesian and distance-based inference returned near-complete polytomies: although the chains converged (ASDSF < 0.01), no branch reached a posterior probability above 0.75, and none of the three multi-language branches (Turkic, Mongolic, or Tungusic) was recovered. The outgroup test made the reason clear: Hindi, which is Indo-European but SOV, grouped with the head-final Transeurasian languages rather than with the other two (head-initial) outgroups, so the features are tracking typological similarity, not shared descent, at this depth. The study contributes 13 new treebanks for poorly documented languages, a reproducible framework for testing how much genealogical signal structural features carry, and direct evidence that, at Transeurasian time depths, this signal reflects typology rather than genealogy.