My memory (which may be faulty) is that the original SSiW - the "Courses" as opposed to the "Levels"- did actually teach "roedd", at least in the early stages.
Although I can remember seeing conversations in the forum at about the time I was doing these lessons that said that in speech either was acceptable.
As far as "he would" is concerned, I seem to remember SSiW Northern Courses teaching "basai".
(I don't know if SSiW Southern taught "byddai").
Somehow or other, I relatively soon became aware that both/either were correct, and that they were essentially regional variations. And I think that is confirmed in Gareth King's Comprehensive Grammar book. Similarly, of course, "byddwn i" vs "baswn i" etc.
It is a potentially confusing area, admittedly. I suspect that books aimed specifically at learners don't give all the variations because they don't want to confuse / overwhelm people (and I think that's a good thing). The book mentioned above is a reference grammar, and definitely not aimed at early learners. GK has other grammar books which are more targeted at learners, and explain it in a slightly more simplified way, and with useful exercises.