Hi @SaraA,
Unfortunately it can be very hard to know how to produce DoE publications because there is so much variation and quality in what is produced in academic publications - I've got a few thoughts on this from my own experiences of publishing DoE works and I'm sure others will add on.
The most important rule: Assume your readers know nothing about DoE or statistics!
Even though it's a popular tool for experimentation, a lot of readers may not have been introduced to it, which means you need to use tools like visualisation to convey what a DoE is doing and to help the readers understand. This is where a lot of authors fall down, with my biggest pet peeve being them including the whole formula in the paper: does that really convey the results of the DoE? Similarly, things like parameter estimates (as you've mentioned) don't really mean much when you've got other tools like your Pareto Plots
I'm going to grab a few examples of how I showed my results to convey some of the ways to show your DoE (shameless plug you can also find the article here

Setting the scene - use simple visualisations to show the structure of the DoE and how the points are being explored - you can do this with Graph Builder or the Scatterplot Matrix when you have loads of factors - this helps readers understand that the DoE is a structured approach to experimentation. Similarly, having a table where you show the coding of your factors (if you're using -,0,+ and axials (a,A) will really help.

Showing what you achieved - before you jump into the regression model and the greater complexities of the DoE approach, you should highlight the real values that you've got, a simple plot in Fit Y by X using something like a Tukey's test is a really clear way to show 'Look how much more stuff I made' using the DoE approach - one of the great strengths of DoE is that it's a structured way of exploring an experimental region, the modelling approach after is another plus! In the example above you can see my '00a' is a lot more productive then the other points - in reality I could stop there because I've got what I wanted!

Introducing the model - as you've mentioned, you're showing the basic information required to prove that your model is sufficient - depending on your target journal, that should be more than enough to prove that you've built a good model and you might not need to dive deeper (unless you're targeting a very statsy journal). If you have material like your studentised residuals and actual by predicted plot - make sure to include them, but maybe in your supplementary information.

Introducing the modelling concept - The Pareto Plot is a great way for a reader to look and really quickly pull apart the significance of your terms and also a great way to introduce more complex concepts like quadratic curvature (X1*X1) and interactions (X1*X2) - the reader can quickly see that 'Blue Line is good' and understand where terms have less importance - this is a great point to link this into your understanding of the system, for example, Nitrogen is highly important to production because of the reliance of the organism used in this paper on it for growth. This helps to show that you're not just running a statistical experimentation method, but that you're using it to understand your system better.


Combine the many ways to show your surface - Personally, I love the Prediction profiler and it can be a great way to show off your system and how it operates, but as you mentioned it can be stunted when you have to present it statically - if you have a simple system, you can show different shots of the prediction profiler with different settings. In my case, I showed the prediction profiler at the optimum (which showed the shape of my factors) and combined it with the Contour Plots to give more understanding to my system. As a tip - if you set your Contour Plot to the same factor settings as is in your Prediction Profiler, the area where the tall grid 'intersects' with the surface (which I added a white highlight to) reflects the surface on the Prediction Profiler!
Consider sharing your results in JMP Public - More and more publications are providing access to the data that formed the results sections (which is great!), I personally really liked publishing my results to JMP Public and including it in my articles - this gives the readers a chance to actually play with the Prediction Profilers and download the available data (here as an example of how I shared my results).
I hope this helps you out and good luck with the review stage!
Thanks,
Ben
“All models are wrong, but some are useful”