Boy can I relate! My husband's mom served about 5 recipes in rotation, all week long. So he was a picky eater: he didn't like her food, because it was bland, but if it had roots and stems, he didn't want to know!

Start with vegan versions of standard dishes: pastas, chillis, soups, casseroles. Things they're familiar with. Don't go too heavy on the faux meats just at first...because they only replace meat after you've been away from it for awhile. A meat eater will notice, I guarantee. Start with say, spaghetti with an exciting sauce of "pizza vegetables" like mushrooms, lots of mushrooms, and chopped pepper and onion and like that in a tomato base. Black olives if they like them. Go for hearty beany soups and chillis, sometimes you can "get away" with TVP in chili but really ramp up the flavour for that. And don't make a to-do about a dish being vegan when you serve it...let them taste it first. Good soup is good soup, whether the broth is veggie broth or something else!

Give them time. Don't talk, cook. Prove that vegan food is tasty as well as healthy, and little by little they'll adapt without a lot of fuss. Two years ago DH would make "puke" noises at the sight of tofu. Now he asks for it!

I can really relate to this because I'm married to an omni who is a VERY picky eater.  He refuses to eat tofu in any form (though I sneak it past him in the best mac&cheese recipe from here), or tempeh, or anything else he doesn't see as "normal food".  It is very hard because I don't want to cook meat for him but he is unwilling to budge.  He will eat vegan chili and soups, mac&cheeze, stir-fry, and he is starting to open up to more asian foods (he recently tried Thai and Vietnamese).  I've also found that rice casseroles and veggie tacos/burritos work well.  I know my husband's issue is just fear of the unknown, but it can be very frustrating.  I was afraid of tofu in the beginning too, but now I eat it just about every day!  It is definitely a great idea to try and veganize their fav recipes, that might win em over...

Drat, I was going to suggest that you try vegan chili & cornbread... it's often a big hit with omnis.  Sure, they know it's meatless, but there isn't the slightest hint of weirdness about it.  :)  Looks like you already covered that base.

Do they like soup?  Pea soup?  Bean soups?  Those might work, and gives you room to serve sandwiches or salads on the side.  A vegan BLT with the above recommended bacon is pretty tasty, and probably won't freak them out much... they can pick off the bacon if they don't like it.  Or just assemble a stack of bread, a platter of different vegetarian salad fixings, and some tasty spreads (mustard, whatever) and let them build their own.  Picky eaters love to build their own sandwiches, tacos, burritos, wraps, whatever -- just give them various options and let them decide how adventurous to be.  Enjoy your own selections with gusto and maybe they will be tempted to go bold.

How about taco salad?  Greens and veggies under, then slightly crushed chips, then beans & salsa -- what's not to love? 

If you're like me, barbecue sauce is your friend.  Use 2 parts or more of canned crushed tomatoes to every part of barbecue sauce to cut down on the salt & vinegar & sugar, and slather your cooked veggies or beans in it... it's delicious on buns.  Just skip the fake meat and go for some nice, recognizable veggies in an easy-to-like sauce.  I like onions, carrots, and cooked lentils in it as my sloppy joe filling. 

As for your polenta... well, I really like it if I let it cool and firm up in a brownie pan, cut it into "french fry" shapes, and bake or broil it in an olive oiled pan until it's crispy.  It's far less "bland" when there's textural variety (crunchy outside, soft middle) and it can be dunked in a sauce of choice.  I recommend you try it again in a different shape.  It might make the difference. 

The kiddo might like it better if he picks it out, or makes it.  You can always stir fry the veggies he chooses (without the soy sauce, of course!) and serve them atop or alongside a baked potato.  Pick the seasonings they DO like (garlic, or onion, or whatever it turns out to be) and stir fry them right into the veggies. 

When I was a kid, my mom "discovered" cilantro -- it revolutionized our kitchen.  Other discoveries like tortillas revolutionized it again and again.  She went through a phase where she put a LOT of chopped fresh ginger and cilantro in all her salads, and I didn't love it as a salad and still don't, but now I think those spicy salads are the reason I came to love both ingredients. 

The DH has deeper issues... hehe!  :)  Not a big deal... pretty soon they will be more excited about new things.  Just make the transition gradual and I think it'll be ok.  Whatever you do, DON'T BLINK!  Don't apologize for a new dish, don't assume it will look weird to them and tell them why, don't acknowledge that something is "weird" and ... well, lots of the time they will still go "eeeeww", but at least they won't come to the table with their minds already made up.

like my parents always said:
If youre hungry, you'll eat it!  ;D

Hi.  I don't follow the "they don't like different" reasoning.

If you were an omni mom serving them grilled tuna on a bed of broccoli raab with a side of mango salsa, you'd feel as though you were expanding their culinary horizons.  So if you're a vegan mom serving them that same dish with grilled tofu instead of tuna, you shouldn't feel that you are imposing your dietary restrictions.

Inculcating your kids with a love of beans and pulses and legumes is probably one of the greatest health benefits you can give them and they will have it their whole life.  Make chickpeas from scratch--be sure to soak them for a long time and rinse the water and cook them slowly until they are extremely soft and then add the salt.  Many kids like chickpeas plain (mine do) and I often serve them with pasta.  Lots of kids--surprise surprise--like lentils.  You can google and find deborah madison's recipe for chickpeas and butterflies and that is usually unobjectionable.

Trish Ross has a whole bunch of bean cookbooks.  She is not vegetarian and the books aren't strictly veg either, but many of the recipes are and they might be a good place to start since they were appealing to her own omni family.