im not real knowledgeable on this particular topic, but i have also tried to grow food plots in areas where i did not have equipment to use. i was fairly disappointed in the results, but i did get some germination. i used some no-till seed, i dont remember what the brand was, but it was some sort of clover blend i think, and it designed to plant in places where you cant get equipment or if you dont have any to use. spray the heck out of the spot with round-up first if you can. killing the weeds down is especially important if you cant do any tilling or plowing.
also, if you wait until later in the growing season, that may help. weed competition seems way harsher in the spring. i actually had better luck waiting until later in the summer, like july or even august, assuming there is enough rain or moisture available. so i would kill the current growth down with weed killer, mow it, and use some no-till seed designed for areas that you cant plow or dig up. you'll get some growth. dont expect a lush, completely weed-free plot, but some growth is better than nothing. i always feel that planting food plots is worth the effort, even if it doesnt come in as full as you would like. good luck. oh, also, if you spray, just be careful not to spray TOO much, i did that once too. burned the soil, had myself a real nice 1/2 acre sand box all summer.