Using API endpoints, does anyone know how to set the order or priority of the component so that when I assemble the baseline component’s, I can set a number attribute on that baseline component, so that when the baseline is created, those entries appear listed in the order of the baseline component ordering attribute?
I think you’d need to configure the order in which you place the components in the XML definitionnof the baseline
Technically thats possible though its done at a script level that builds the XML like @JasonWalker mentions. I’m using PowerShell to manage baselines which basically generates the baseline XML that is then posted via REST. All the fixlet ordering and deciding what component group the fixlets go into is done so in the PowerShell script, eg servicing stack update fixlets go into a dedicated component group ordered by the fixlet release date, patch fixlets into a different component group again ordered by the fixlet release date.
Any chance you can share your code (minus embedded creds of course)?
Not easily as its a multi feature script with lots of functions I created for the tasks we use inhouse and are trying to automate. I’ll try and pull out the bits for the baselines and strip out any company specifics. I avoid storing credentials in the script so there aren’t any of those to worry about 
Send it all if you want
I have a working baseline example now, you can skip sending your code if you don’t want.