Start with one number
Before any model, agree on a single definition of a qualified lead and count it in one place. Most attribution arguments are really definition arguments. Once the definition is settled, the arithmetic stops being contentious.
What you can safely ignore
You do not need multi-touch modelling to run a good marketing programme. You need clean events, deduplicated conversions, and consistent channel grouping. Everything past that is refinement, and refinement on dirty data is theatre.
Making it defensible
Write the model down: what counts, what is excluded, and where the known gaps are. A finance team will accept an imperfect model that is documented far sooner than a sophisticated one nobody can explain.