I would like to customize the fields that come up for end users when they fill in the details for JiRAs on a specific project URL
We wrote an article a little while ago on different options for using web forms with Jira, which might be helpful.
Our app ProForma allows you to use forms to create or update issues in Jira. You can build a form for each issue/request type in Jira and use conditional logic to dynamically show and hide fields on the form. You can also capture as much information as you need, without having to create a custom field for each question. There is also ProForma Lite, which is free and has all the same features as ProForma, but only allows you to design three different forms.
However ProForma can't trigger a specific form on a URL (but I'll add it to our feature backlog).
Full disclosure: I’m part of the team that makes ProForma.