My understanding is that the “Increase indent” button uses the default tab stop positioning. My tab stops are set at 1cm intervals, but my increase indent button increases by 1.25 cm and not the tab default of 1cm. Any ideas how to set the increase indent default?
From the top menu select: Format -> Paragraph... -> Tabs and set it to 1cm there.
You can also make it persistent by applying it to the default paragraph style: View -> Styles and Formatting, right click on the Default Style, go to the Tabs tab and set it there.
Changing the tab setting in paragraph style doesn’t change the default stops for the increase/decrease indents. I did resolve the problem in discovering that there is a default tab stop setting in Tools>>Options>>LibreOffice Writer>>General Changing the tab stop setting controls the tab for the indent button.
It is not recommended to use tab stop to indent text, because that method is prone to formatting inconsistencies. Writer provides a more powerful method to manage indents (and a lot of other options, like tab stops): the use of styles.
When you modify or create a paragraph style, on the Indents and spacing section you’ll find all you need to set a consistent indent for all paragraphs using that style. On the Tab stop section you can also set, well, tab stops 
There you can set not only the tab stop positioning but also their alignment, filling character, etc.