> The obvious alternative to gradient descent here would be Bayes Formula

If you know a little about the math behind gradient descent you can see that an embedding layer followed by a softmax layer gives you exactly the best Bayes estimate. If you want a bit of structure, like every word depends on previous n words, you get a convolutional RNN which is also well studied. These ideas are natural and elegant but maybe a better idea is to comprehend the research already done to avoid diving into dead ends too much.