I understand your issue now.
Once the task has been created in JIRA will you ever need to change those fields from monday?
If not, this could be relatively straightforward to solve by using Integromat (or custom app) to create the initial JIRA issue then allowing the current monday JIRA integrations to handle the linking and further updates. If so, you might want to forgo the built in monday/JIRA integration completely and handle the entire integration through Integromat (or custom app).
The built-in monday/JIRA integration makes the setup of joining monday to JIRA much easier. But there is nothing significantly magic about it. It can done using the webhooks and APIs of the two systems. The fields that monday has not yet implemented are more complicated in that they require tighter integration. Components, for example, can not be set to just any value. Integrating this field will require data validation and error handling, etc.
Depending on the specific details of your situation you may be able to make certain assumptions and/or restrictions regarding these “complex” fields. Thus making the integration for your situation easier.
The bottom line is that it is POSSIBLE to work around the current built-in monday/JIRA integrations. But, the question is will it be worth it considering the details of any given scenario.