Zoho CRM integration: mapping form fields to custom CRM fields

Dear Sir/Madam,

I have a question about integrating Jotform with Zoho CRM.

When I activate the integration with my Zoho credentials and go to the phase where it asks me to map out fields in the form with those in Zoho CRM, I can only map them to standard fields in a Zoho Lead or Contact module. The thing is though that my Lead and Contact modules are heavily customized and would need to have exact field correspondence between both applications. Is it so that the Jotform integration only supports mapping to standard Zoho CRM fields? Whatever I do inside Zoho does not seem to affect the available fields in the integration. 

Thank you for your help.

It will try to list all of the fields that it could find, but if you can show us how the other fields are built we could recreate them and see if we can create the integration with them.