Ooh, a new Rensslaer HOI3 AAR co-inciding with my getting back into the game. Sign me up!
I have a feeling there'll be an odd tension in this AAR between your stated aims (making Germany a powerful and respected European nation once more) and what we want to see happen (you getting dragged into a big war). The 'win' condition for you is to get to the end of the game with a strong and peaceful Germany, but I for one would be happier to see a bit foreign adventurism, even if it was purely defensive.
I agree with your basic premise that the UK and France would be willing to countenance German rearmament to a degree. A canny German government might make much of criticising Italy's expansionism in Abyssinia (although that starts before the game begins) and be similiarly critical of Japan. However, I suppose that risks isolation from potential allies while not doing enough to reassure France and the UK.
On remilitarisation of the Rhineland, wiki has this to say, which suggests that it wasn't out of the question. However, it might be wise for a more dιtente-seeking German government just to forego remilitarisation altogether. After all, the Maginot line suggests France's priorities were essentially defensive, so no sense provoking them. What better way to convince them that your military build-up is related to a fear of the Soviets than to allow your defences in the west to remain weak?
I'd say a Germany that didn't remilitarize the Rhineland and that sought to assert influence in central Europe through diplomatic means would quickly be seen as being on the side of angels if the Soviets started throwing their weight around (Winter War, occupation of the Baltic states and possibly an attack on Poland). This should turn out to be a very interesting political situation!