Multi Class Classification on large dataset with over 600 classes
Generally I have seen SVM perform well with Text Classification tasks. Why don't you first try with taking TF-IDF in place of Word2vec.
Let's say you have a sentence D1 with terms T1,T2 and T3. Represent it as TF-IDF first and classify. This link might help https://www.analyticsvidhya.com/blog/2018/04/a-comprehensive-guide-to-understand-and-implement-text-classification-in-python/
Then you will know if the problem is with memory issues or your word2vec approach.