Mucilage. It’s called mucilage.
Actually, let me expand on okrology.
First, selection. Large okra = bad. The larger the pods get, the tougher they are, and truly large okra can be bitter as well. Southern rule of thumb: don’t buy okra any longer than your pinky finger. They’re perfectly tender, yet firm, at this stage.
Second: rinse them well, to remove the prickles. If you’ve ever picked spiny okra, you’ll know of what I speak. Okra can be painful. The fruits have fewer prickles, but it’s best to make sure they’re all gone. A good rinse should be enough.
Third, the mucilage. The “slime” is a very large glycoprotein (a protein with a branched group of sugars attached,) which has been associated with scrubbing cholesterol out of blood. Mucilage = good. However, since many people find it objectionable, note that dry heat tends to minimize it. This makes grilling a perfect method of preparing okra. The mucilage breaks down under dry heat (and I have no scientific basis for this, but I suspect the sugars from the glycoprotein are released and can be caramelized during cooking. Grilled okra certainly has a subtle and complex sweetness.)
Fourth, grilling okra results in a wonderful, delicately sweet vegetably flavor. Think: asparagus with beautiful little pearly seeds in it. And no, they should not be slimy. Moist, but not slimy.
Yeah, I know the big ones aren’t desirable - I think the farm must have missed a couple until they’re too late. I’ve got some appropriately small ones, but I’ve also got some honking big badass ones that I may just have to throw out.
Sure, toss 'em. Eat the small ones that you may actually enjoy. 
Like Mrs. Plant, you don’t have to tell anyone, and can always deny it later.
As the man said, overgrown vegetables aren’t good. I was given some very large zucchini that I ended up stuffing. They had large, ugly seeds that made them not good for much else.
You can do it in the oven too, I presume?
I do essentially the same thing with asparagus and brussel sprouts and they’re like candy too. Crispy, slightly charred, salty candy.
I put them in a Ziploc with olive oil, kosher salt and fresh ground pepper and shake to coat. Dump on a cookie sheet and bake at 400 degrees, giving them a shake and a stir every 10 minutes or so until fork tender.
I do the same thing with potatoes too. I’d oven roast everything if I could!
Pickled okra is crisp and briney. No slimieness, excellent garnish to New Orleans fare.
Yep. The oven should work just fine.