I think your problem is one of terminology, not functionality.
If you want to record a new potential sale for an existing Account or Contact, the most obvious thing to do would be to create an Opportunity.
If for some reason you want to create a potential potential deal, and want to use a Lead to hold this so you can do a more formal pre-qualification before you get to Opportunity, then just create a Lead linked to the Contact and Account. Since there is a relationship there already, you cold do this by adding a sub-grid on the Contact form, or adding Leads to the navigation on the form (like any other child entity).
You don't need to "convert" the Contact, keep that as it is and just add another record to represent the possible new sale.