Ajaxy entity reference views filter by entity reference view
I'm not sure this question has a good, Drupalish answer.  I've got a crazy idea, though, that you might try.

Instead of letting your users go straight to node/add/typeA, send them first to a custom page where they choose their size. That link will then send them to the node add screen with a TID tacked onto the end, like /node/add/typeA/34.

On the node creation page, your custom module will automatically select the right Size term based on the URL path, and disable the widget so the user can't change it.

In your Entity Reference view, when you provide a default value to your contextual filter, instead of "Taxonomy term ID from URL", simply choose "Raw value from URL" and set the Path component to 4. With any luck, the Entity Reference view will get the TID from your modified URL and show the right list.

When they try to edit that node after creation it gets a bit tricky. You could just forcibly redirect the path to node/[nid]/edit/34 and do the same thing, but now you've made it so the user can never change the category after they select it the first time, which is bad. Maybe you can hijack node/[nid]/edit and send them to your custom page again? I've never seen that done before.

This whole idea kind of craps up the usability of the site, but it's the best idea I can think of, short of writing your own custom AJAX stuff to provide your argument to the ER view manually, rebuild the form, etc.