graph theory – How to prevent spanning trees from spiraling

Spanning trees and especially minimum spanning trees are the anchor point of a whole class of TSP heuristics, most prominently the Christofides algorithm.

I noticed however that there may be MSTs for which the generated tours may not even be two-optimal, namely if some or all of its leaf nodes would be encircled by tree edges:
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the Christofides algorithm would connect both leaf nodes with an edge, generating a tour with arbitrarily many self-crossings.
Interestingly that spiraling in MSTs apparently isn’t honored in benchmark instances for TSP heuristics.

Question:

is it possible to efficiently calculate vertex weights that, when added to the weights of adjacent vertices, guarantee that the tours generated from the MST will be two-optimal?