Managed sweetcorn here as well, but I suspect small in comparison, even got some passion fruit a few times. Got a couple of Kiwi plants(boy/girl) nothing yet and do they ever grow fast !
Re. carrots, shady patch and light soil, if warm white fly will have them fast so can disguise smell between onions or other items, funnily enough Marigolds are quite helpful.
Bok Choy is lovely, might give that a try, good idea.
Stanski could always put his name down for an allotment locally and then the bulky stuff could be done there, quite an amusing idea to role up to an allotment in a Zed.