It seems to me that it should be fairly easy to change the settings of Default.nb used as the Stylesheet for new Notebook sessions. But apparently it is more of a big deal to do this than I anticipated. As you state the Option Inspector seems to be a good place to do this. Attached is a screen sheet of Option Inspector, not quite the same as you indicated. Unfortunately, searching the menu is rather cumbersome in that the menu window is very small and cannot be expanded. I went through the entire menu but was unable to locate DefaultStyleDefinitions. But maybe I am missing something very obvious. The initial step of attaching a customized Stylesheet (created with Menu/EditStylesheet/Install Stylesheet and accessed by Menu/Stylesheet) to each new Notebook is no big deal. Just didn't want to do that extra step if it could easily be avoided. Again, thank you for your efforts...

Attachments:

You can't edit or change the Default.nb, or at least you shouldn't. It's part of the Wolfram Mathematica Installation and probably protected.. You can edit the stylesheet initially attached to your working notebook. Then install it under a different name, SteigerwaitDefault.nb say.

I'm not sure what's going wrong with issue#2. I just edited the Input style to Verdana Regular (which Mathematica changed to Plain) and it was recognized in the stylesheet and in the notebook. But I tried Lucida Calligraphy and that was recognized in the stylesheet but not in the notebook. When I added FontFamily -> "Lucida Calligraphy" to the underlying options in the notebook cell it did recognize the font. So here I think you did find a bug. Some fonts work and some don't.

Once you attach a stylesheet to a notebook it will automatically be used. But new notebooks will use the WRI Default.nb. I think you can change that by using the Option Inspector. Select Global Preferences. Then look in Global Options, File Locations, DefaultStyleDefinitions and change "Default.nb" to your preferred stylesheet. I think you have to click on the little gray square and then go to the installed stylesheet.

Use Menu, Format, Edit Stylesheet and make your change. But I think you want the Face to be Plain, not Regular. This change should alter the look of the entry in the Stylesheet and also in the notebook. If you just want to attach the style to the specific notebook you can close the stylesheet at that point.

If you want to Save the stylesheet for general use in other notebooks, then use Install. This will install the notebook in your

$UserBaseDirectory/Mathematica/SystemFiles/FrontEnd/StyleSheets 

folder. It will appear on your Format, Stylesheet menu.

But the stylesheet will still be attached to your notebook. Now use the Stylesheet menu to specify the new installed stylesheet.

If you are sending your notebook to someone then you will also have to send the stylesheet (and tell them where to put it) or you will have to attach it again to your notebook.

If you are also going to have other things, such as a package, and are working on some specific application, then you might want to create an application. These also have a place for stylesheets and can include notebooks so you could just zip up the application and send it to another person. The notebooks would automatically use the stylesheet and you wouldn't have to give any special instructions. I describe how to build an application and stylesheets at my web site. A Mathematical Style. Few people seem interested in this however.

Long answer: With considerable work, if stylesheets have multiple inheritances.

Short answer: If you have one stylesheet that inherits from a Wolfram stylesheet packaged with Mathematica, then the following will embed the stylesheet myStyleNB in the notebook myNB.

 SetOptions[myNB, StyleDefinitions -> myStyleNB]

The notebook myNB should be an open NotebookObject[], such as returned by EvaluationNotebook[]. I usually execute SetOptions[EvaluationNotebook[]...] and then delete the cell. You could also choose the notebook from the following popup menu:

PopupMenu[Dynamic@myNB, Notebooks[]]

Now, myStyleNB should be a Notebook[] expression, such as returned by NotebookGet[]. Something like this:

Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
  Cell[StyleData["Section"], FontColor -> RGBColor[0, 0, 1]], 
  Cell[StyleData["Input"], FontWeight -> "Plain"]}, 
 WindowSize -> {808, 911}, 
 WindowMargins -> {{-1570, Automatic}, {-102, Automatic}}, 
 FrontEndVersion -> "14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", 
 StyleDefinitions -> "Default.nb"]

If you have both the notebook and the stylesheet open, then you can select each and set the stylesheet with the following:

PopupMenu[Dynamic@myNB, Notebooks[]]
PopupMenu[Dynamic@myStyleNB, Notebooks[]]

(* execute the following AFTER setting both notebooks *)
SetOptions[myNB, StyleDefinitions -> NotebookGet@myStyleNB]

I also found this presentation released this week that had technical difficulties and poor production values, but is nonetheless very helpful.

https://www.youtube.com/watch?v=92Rgzc9KV2w&t=3s