As a young teen working on a farm we used to hoe 1/4 mile long rows. With practice, you could do 2 rows in the morning and two after lunch. That was a mile of hoeing in one day. Hence the meaning of "a long row to hoe" saying
Nowadays, doubt I could do 1000 feet in a day, or before my arms fell off.
The triangular hoe or a triangular with flat tip worked best. The slight curvature someguys made, didn't work for me.
We sharpened them everyday and honed them a bit at lunch too.
I like the looks of the Action Hoe HG has pictured.
The pole bean thing with corn isn't as good for the beans as it is for the corn, but is okay. Bush beans work really well with corn, I personally can recommend it, it works great. The squash corn bean mix, well good luck with that one also and good luck keeping the bugs and mildew diseases down, I've not had much success, jusdt wasted time space and seeds.
If anyone has the 3 plant technique down, please let us know how, because it intrigues me.
These days, I would till between the rows and cardboard paper if there was room between some of the plants, but you have too long a rows and likely not that much paper.
So leave it go, the corn eventually outgrows the grass, with some loss of production. And plow that grass deep next year.