If you are going to use roundup, might as well go ahead and use a pre emergent herbicide as well, like treflan if is still made. That one two punch will kill both the grass and will kill the weed and grass seeds that would otherwise germinate later.
Personally I would do neither. I would till during a dry period. Wait about a week, and till a second time. Would then rake out as much grass as practical, plant my perennials and mulch around and between rows. Also I would consider doing this in smaller, manageable blocks rather than attempting the whole planting at once. The new perennial beds will likely need large amounts of water for most of this summer.
I would also consider having a skirt or barrier around the entire site, using black plastic covered in some appropriate mulch. That will keep the grass from encroaching from adjacent areas. Finally, IMO mulch over grass for the most part does not work. The grass simply grows through the mulch, smiles at the new friendly environment, and then proceeds to dominate the lanscape. If plowed and mostly removed first, it is much easier to stay ahead of any of those pesky grasses as they try to penetrate the mulch and re-establish themselves.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.