Access to a Haas mill ? Very nice ! Also suggests you may have a good source of raw materials.
I'd keep the headstock off the donor lathe and whatever else suits your plans (motor, etc) and build the rest but that is the long road and
you may want to be running sooner. Conversions are usually a collection of compromises, making things fit what already exists.
As far as smallish lathes having globs of excess material, I don't think engineers think that way.
My 2 cents and worth exactly that.