My starrett surface gauge, like you are building, is hard steel. The bottom face looked original but wasn't flat.
I tried scraping it but it kept chipping my carbide. Finally used stones to finish it.
About 4 months ago I bought a Starrett 665 indicator set.
The base is cast iron and not hard. Had to scrape it in as well. Haven't done the sides yet.
A flat pull scraper works well for tool surfaces that will be used on a surface plate.
Almost forgot.
The glue on paper backing can introduce high or low spots.
If you wet the surface plate and press the plain backed paper to it, it will hold well and
be more accurate.