I'd eliminate the weeds first because if you rotovate perennial weeds back in to the soil they'll just grow back

Exactly.

And they will multiply, too! Made that mistake with bindweed back in '75...brr! Took me a decade to get rid of it, and it doesn't even grow well here in the low desert!

How about covering the area with landscape fabric or similar for a few months? This will kill all the annual weeds and grass and then you will have more hope of clearing it all. Also, try to organise the area into beds about a metre wide so that you can work them from both sides without treading on the growing areas. This helps a lot with soil structure and waterlogging, to a certain extent, as the soil drains better if untrodden. It also means that you can work on one bed (less demoralising when you can finish one section and not see the whole veg garden streching out, un-dug!!) at a time and rotate your crops correctly.