We always do TS for lunch and dinner--having a break to sit and recharge is great for all of us. And we've eaten at every signature multiple times (I miss the deluxe dining plan) except V&A because no kids allowed and Takumi Tei, because of the price tag and the limited kids menu. You really can't go wrong with most places, but I've listed some of the places we've found were the best experience in terms of solid kids menu, atmosphere, and great food/ambiance for mom and dad.
California Grill--our kids loved the unique kids menu desserts and getting to watch the sunset from the rooftop observation area.
Hollywood Brown Derby--has one of the most approachable kids menus for a signature restaurant (our kids were thrilled with their hot dogs) even though the adult food is very sophisticated and the restaurant is gorgeous.
Be our Guest--what is more than fun than eating "the grey stuff" for dessert inside the Beast's castle? If you aren't seated in the "West Wing" definitely stop by to see the the rose petal fall and the lightning magically change the painting of the prince/beast. Note this is a prix fixe menu (adults and kids alike need to pay for appetizer, entree and dessert)
Tiffins--This was our favorite food as adults (much better than Jiko, though similar menu concept), but it is a little more adventurous of a menu for the kiddos, so you'd need to check it works for them.
I left off Yachtsman and Narcoosees and the Disney Springs signatures even though they were perfectly nice meals because I feel like there is not much that is very "Disney" about them--we have so many restaurants like that at home (although if you don't have a Jaleo where you live, that is worth a visit). Loved the character breakfast at Topolino's but you said you're not interested in character meals--and we weren't that impressed with the dinner we had there.
Don't let anyone discourage you--if you are midway through your trip and finding it is not working for you, just cancel some or all of your remaining ADRs (no penalty if you cancel before midnight the night before). Our kids are never too tired at dinner time because we are conscious about going at a slow pace during the day, using a stroller for our youngest, and take mid-day resort breaks--which frankly is a good idea whether you are eating a TS or not.