Is there paint without texture?
I would try sandpaper or even an environmentally friendly (low fume) paint stripper. Other solvents might also be a worth a try, for example mineral turps for oil. Another option is to use a heat gun to soften it and then scrape it off with a flat bladed scraper used for plastering. I did this today successfully, just don’t touch the blade as it gets extremely hot after being near the heat gun. 

Unless you can add a very thick layer higher than the depth of the original's texture, I think you'll have the same problem. 

If the canvas is mounted on board, it is easier to scrape off. If it's a stretched canvass, you might need to be more careful in the scraping part -- you don't want to catch the (sharp-edged) scraper in the canvass and make a tear.