Greco these days is mostly "pretending to be active in the stand-up" and then scoring in parterre. There are only very few outliers who have reliable takedowns from stand-up, and if so, rarely more than 3. For example, Frank Stäbler had a very successful run at a number of World Championships, and basically the only move he hit standing in international competiton was the arm drag. He did have other throws of course, in national competitions he'd even hit flying squirrels, but he seems to have considered those too risky for bigger championships.
As for "Judo style" throws in international wrestling, I'd say that for the largest part, they are variations uncommon or even illegal in Judo (Kani Basami, Kawazu Gake) or were introduced to Judo from other styles to begin with (Mongolian Uchi Mata).
Cross training is actually not that common anymore in my experience and from what I heard (I wrestled in Germany and Austria, but had coaches from a number of places in the former Soviet Union and teammates as well as opponents from all over Europe, the entire Caucasus area and even Mongolia), partly because the rule changes in the various disciplines are aimed to make them more distinct from one another. I only met three guys who also did Judo or Sambo (not counting myself) over my whole career. It's more common for someone to quit one thing and take up another, but recently, BJJ has soaked up most of these people. However, there was more crossover up to the 80ies and 90ies, and the various stylistic influences have blended into the main styles to the degree where it's sometimes almost impossible to say who got what from where.
