Good, symmetrical, quarter sawn lumber is about as stable as you can get, but it’s very pricy, and most likely not even available in 14' long maple 2x12's. I can guess 90% ± of the time how to lay flooring and decking to get it to cup, convex up, so it won’t hold water. But, it’s screwed or nailed down to inhibit most other forms of warpage at regular intervals. There really is no answer to the question you are asking, it’s a crap shoot, multiplied by the number of 2x12's you have in your assembly. And, you have to get with the Arch. and explain this, you can’t guarantee something like this, and you end up looking smarter, not incompetent, for bring this to his attention at this point in the design process. Get with him and find out how critical perfection is and what he’s willing to pay for it. Or if you are worried about nothing.
Your sketch is good and really helps with understanding, but that isn’t what I would have guessed a lattice was. But, you still leave much to the imagination. You show the glue lams as being 2' or more deep, so probably a fair distance above the fl. and I assume your fake joists only carry their own weight. Can anyone see a little warpage or even see that they are maple, for the premium that’ll cost, and given the lighting conditions? Certainly hardness and textural appearance shouldn’t be a big deal, or are they? Color contrast you get with stain. Your lines of blocking with a 1x flange t&b would help, but I can’t tell you how many. And, that introduces an aesthetic feature which I better let you and the Arch. fight out.
This looks like work for a finish carpenter, not a structural engineer. And, he would make these out of two side pieces of 1/2" plywd.; with 3/4" or 1" plywd. blocking btwn. and at side piece butt joints; with a 1x width + 1/4" ripped (1/8" reveal each side) for the t&b flanges. And, if he was real cleaver, he would cut a notch in each end of the top flange about 1&1/2" long, so he could slide these up over a knife plate, same thickness as inner blocks, and screwed to the glue lams. Thus getting rid of the ugly Simpson joist hangers.