I'd argue that the Germans kept that position until late Summer/early Autumn 1940 - it was not until they had defeated France and knew the Soviets would be next that they started courting Finland, selling captured French arms at cut-rate prices, asking for transit rights for troops from Norway and releasing a lot of the impounded Hungarian and Italian arms.Rather than saying that the Germans were anti-Finland, I'd rather say that they considered Finland a mere pawn to be first traded, and then utilized. Their stance during the Winter War was to hold on to their bargain with the Soviets, as you said, and thus stop aid to Finland, etc. But as soon as Finland could come out of the war (more or less) intact, Germany started recruiting the Finns to their side against the USSR. With regards to Finland, in 1939-41 the Nazi leadership then arguably managed what is perhaps not entirely known as the hallmark of Hitler's diplomacy - cool, calculated pragmatism as to how the Finns might best serve the wider Nazi goals.
The Finns pursued the potential union with Sweden as late as September 1940, when Jarl Wasastierna officially made a request for a union with the Swedish foreign minister. German troops arrived in February 1941 (although transit had been agreed in September 1940) after the Soviets declared the union a breach of the March peace in December 1941.