I guess one needs to re-express quo()/rem() in terms of pquo()/prem() to make that work?

Only your question made me aware of prem(). Now, that seems possible but prem() itself appears to have problems:

prem(x*y^3,y*x^3,x); x*y^3

This would (according to the tutorial) satisfy x^(-3)*x*y^3 = y*x^3*q + prem (=x*y^3), so q = pquo() = (x^(-3)-1)*y^2/x^2 which doesn't seem right. There is also the problem of quo() returning a fail (decompose_rational() needs it) which surprised my computations, giving an error, something with commutativity, and I needed some time to see that I was working with a fail that I got from quo(). Thanks, ralf