It sounds like your weeds have gone to seed. You will have a 100 times more weeds for the next few years. But that just means more 'mulch/compost'. I am sure there is an ultimate perfect way to do stuff, but just leaving the stalks standing is fine and is actually encouraged. you have cut them above the ground that is also fine too.
alot of folks cover their garden beds in the winter with
straw. I am a big fan of more
carbon soil life, in any package that it comes in. Maybe you can even plant some winter cover crop this week depending on your climate. If you want to concentrate all this chop and drop from say 20,000sqft to just a 1000sqft
garden bed it would make sense to collect it all and then transport it and compost it. Maybe if you wanted to kill some/most of the opportunistic seeds in there you would do hot compost in at least a 3ft x 3ft x3ft pile.
Iterations are fine, we don't have to be perfect
My 2nd Location:Florida HardinessZone:10 AHS:10 GDD:8500 Rainfall:2in/mth winter, 8in/mth summer, Soil:Sand pH8 Flat