Give it a go. What have you got to lose by trying? They come up in a few days and grow fast in warm damp weather. But they like a good diet and they might suffer in competition with the sunflowers which are already established. Also they will head straight up and not really cover the SF stems much. Not sure why you thought the SRBs would endanger a child, unless they strangle her. She'd have to crunch her way through a lot to have any effect. I would have thought the tomato leaves were more 'dangerous'.

Here is a link that might be useful: Runner bean info incl. toxicity

Thank you for the link. I was worried about any mature pods that might be hanging within her reach, as toddlers tend to put everything in their mouths...my GS picked a "berry" from a very hot pepper plant at an arboretum when he was that age. Luckily it was not something poisonous. I guess I was being overly cautious. In any case, no worries now as they have moved.
I'll go ahead and pop a few SRBs in and see how it goes. I don't have anything else that could hide the bare spots. Either way, I don't think it could look any worse than it does now.
Thanks again.

Noinwi, it took about a month and a half to two months for my Insuks Wang Kong runner beans to get up a trellis 6 feet and set many flowers and quite a few pods are well filled by now. Last year they attracted green hummingbirds. You could have the first flowers in as little as three weeks.

Also last year I would not eat the raw pods, they were too strangely thick and rough looking compared to the usual common bean. This year I tried a couple and they were surprisingly faintly sweet tasting. Are runner beans usually sweet compared to common beans?

Have you noticed any Japanese beetles, grasshoppers, or large caterpillars like hornworms on your plants? Any of the above can destroy a lot of leaves quickly.

HD, the pest that's doing the most damage is the cabbage looper. I have to wait a little longer to buy some Bt, and I don't have anything that's working on them, so I'm just trying to pick them off, but it's hard because they're not that large and they're the same color as my tomato plant. I could never find what was damaging the sunflower leaves...maybe slugs, but that wouldn't have been my first thought because the slugs around here are so tiny(I come from SLUG country, the PNW)and I never saw any slime. I saw my first JB of the season yesterday...they are attracted to my basil, so much so that it kept them away from my beans last year.
I popped in a few SRBs near the base of the sunflowers and we'll see what happens. I've found that the SRBs are best eaten quite small, as they get stringy(and hairy)quickly, so I usually use them as ornamentals.

Plain dishsoap in a sprayer is what is used by professionals on killer bees. I wonder if it would kill your cabbage loopers.

Don't know about sunflower leaves, but check the flower faces at dusk for earwigs. They are attracted to the seeds. Earwigs and other burrowing beetles can be baited with sugar, grease and borax. Borax won't harm pets but put it where dogs can't get it anyway. I put it inside a concrete block with another block flat over the top.