I think what you've described is a primary in two "sections", rather than a bifilar winding, as such.
Winding "sections" are usually wound as complete layers on the former, interleaved with sections of secondary - often a layer (or several) of primary on the inside, a layer of tape, a layer of secondary, more tape, another layer of primary, more tape, and then a final secondary layer on the outside. The different sections are generally brought out to the pins and connected in series.
In contast a bifilar (or multifilar) winding has several wires electrically and physically in parallel, so that there is no voltage between them. They are just insulated by the enammel coating.
You can even have multiple multi-filar section, if you want!
You're right that the multi-section winding is done to improve the coupling between primary and secondary. As I understand, both these techniques relate to avoiding the problems of skin effect, so are really two sides of the same coin.
There's more than you ever wanted to know about the subject here, in the Magnetics Design Handbook:
https://www.google.co.uk/url?sa=t&r...25.pdf&usg=AFQjCNHwlTHWN6x82i1h4X6fsOhmC-8Lyg
Personally I would have rebuilt the transformer as original (with 2 sections), but it looks like you've been sucessful, so well done!
As far as I can see, if it manages to supply the full load with good regulation and without overheating, then it's working perfectly well. I hope it's still working.