If you hold off on popping any GWAM before you get your factories up you can go Autocracy and take the mini-tourist bomb policy. Early on a 250 tourism bomb every time you get a GWAM can get you back into the influence game in a hurry. You don't even need to make them great works, you can use them for culture bombs and golden ages. With a good setup with gardens and national epic you could pop the first two of each type in less than 35 turns. That would nab you 1500 tourism with everyone, much better than the 12 tourism per turn that you'd get using them as early great works.