So, indeed all I had to do was make it grid-column: 1/8 and grid-column: 8/13 for it to span over the 7/12ths and 5/12ths of the .page-grid-layout respectively. And span 7 / span 5 work too, as long as you don't try to use a variable for the number of columns and inadvertently do

grid-template-columns: repeat(var(--columns, 1fr));

instead of

grid-template-columns: repeat(var(--columns), 1fr);

That was surprisingly difficult to debug :)

Thanks Mikhail and Ori Drori for the answers!