Copying Field Data (Primary Campaign Source & Custom Field Data) from Contact to Associated Opportunity

My sales team have been creating Opportunities outside of lead conversion. This is fine, but there's a few fields the Marketing team needs that are not populating when creating Opportunities from a Contact page. I have decided to remove all new Opportunity buttons except those on the Contact record to ensure they are creating them there as this ensures the assignment of a contact role.

I have 3 essential custom fields that I need to copy from the Contact to the Opportunity when manually creating an Opportunity outside of Lead Conversion. 

I created my own action button on the contact page to create the Opportunity and capture the field data I need using the predefined field values, but 'Primary Campaign Source' does not show up in the list of available fields for me to choose from. When creating an Opportunity using this custom button, this field has no data even if there is a Primary Campaign Source.

The standard "New" button on the Opportunity related list on the Contact page, grabs Primary Campaign Source but doesn't grab the 3 custom fields I need on creation. I can't find a way to update the standard "New" button with predefined values for the 3 fields I'm missing. Pretty sure this isn't possible anyway.

So, the way I see it, I need one of the following solutions;

• Flow that updates the the 3 fields I need after creation using the standard "new" button
• Flow that updates the 'primary campaign source' after using my new custom button
• Some other elegant yet simple solution I'm overlooking?

My issue is, when creating a flow for either of the first two options, I can't find the field data in the list of fields from either a "get records" action or a simple "update" action. It's almost as if the associated contact to an opportunity doesn't exist in the flow? 

I feel like I'm overlooking something here, but I thought having a contact associated with an Opportunity through the contact role would be enough to make all fields on the contact record available for this. Please help!