I have not heard of, nor have I tried, either of those plugins from barn2.
My best guess is that there should be no problem with the Private Store plugin. As far as the product table, that really depends on how they are getting their data to show in the table. As long as they are doing things the proper WooCommerce way, and using WooCommerce methods & functions to get the prices, then that plugin should work fine with my plugins. If, however, they are pulling the data, such as prices, directly from the database instead of using WooCommerce functions, then they would be bypassing the filter hooks that WooCommerce has in place that allow plugins like mine to alter the price based on the current user/role.
Have you already purchased those plugins? If so, you could email me privately and send me a download link, and I could test it here on my development system. Alternately, you can order my plugins and test them on your own dev/staging site to see if they are compatible. If they aren’t, then I would either see if there is a fairly simple way for them or me to add compatibility functions, or I would give you a refund if you would rather use their plugins than mine.