So this question peaked my interest. I didn't realize we couldn't see the custom fields on the job flyout until you mentioned it here. That got me curious so I went looking and from what I can tell there is no way add your custom fields so they adhere to the job flyout.
Even though there doesn't seem to be a way I would definitely put this in the ideas page and I would happily vote for it!
I am just here to say I appreciate the questions you have set up on the call booking screen! I appreciate how you remind the CSR to use empathy and also how you say "To get you back up and running as soon as possible, may I ask a few questions?" That is a great way to lead into the questions we have to ask! 🙌
We also have custom fields set up when on the call booking screen (such as the method of payment the client will be using) and they do not transfer over to the dispatch board view. When I go into settings and take a closer look at ours, I see you can select to add it to the project record however, I do not see an option to configure it so it appears in the job summary. If you would like this custom field to appear in the job summary instead for the dispatchers, maybe consider moving it over to that area instead?
Sorry I cannot be of more help to you!