Prepping a vegetarian picnic without a grill

I would cut an X in the portobello caps for even cooking and broil or roast. (brush with olive oil first). You can roast the other vegetables too, then mix together as a "samfaina", (a Catalan dish of mixed roasted summer vegetables) to be served cold (or room temp). Dress with minced parsley, olive oil, salt, lemon juice or white wine vinegar, and minced capers. (This does normally have cubed fresh uncooked tomatoes, however, as well as roasted eggplant and red peppers). I agree that roasting will give the best flavor.
A quinoa tabbouli (or other quinoa salad) would be great as would a chickpea salad (lemon juice, olive oil, salt, pepper, minced parsley, paprika, optional garlic)

You might add a bowl of olives, various breads and/or flatbread as mentioned below. A red pepper dip (there is a marvelous one here: https://food52.com/recipes/14420-jean-anderson-s-sweet-red-pepper-paste-massa-de-pimentao). Hummus optional.

Roast the portabellos whole. Also roast the other veggies with a basic olive oil/salt/pepper.
Cook the quinoa in half water half vegetable broth. Once done cooking and cooled stir in chopped fresh herbs like some basil and parsley and small cubes of the mozzarella with some sliced almonds or sunflower seeds and add a bit of a basic vinegrette and stir together.
Pile the quinoa into the portabello caps as an “entree”. Serve extra quinoa mixed with soft salad greens.
For the roasted veggies i would leave as is and serve with a side sauce for dunking like a white bean and basil dip or your pesto.
All of this will be fine served room temp or chilled and made up to a day before

Roasting your vegetable first all give them the most flavor. For the root vegetables, when they come out of the oven toss them in a vinagrette and serve everything cold on a platter. Make a pesto to serve with bread. The Quinoa can be prepared like a tabouleh. Mozzerella is always a choice that pleases most palates. Feta will travel well also, also good in most crowds. Goat cheese is too soft and will make a mess of everything unless you put in a jar.

For me, picnics mean indulgent good food served outdoors.
Start with the vegetarian drink par excellence, chilled red, white or rose. For the abstainers, a good fruit punch or fizzy water.
Main dish: room temp quiches, galette or pizza.
Or, baguettes, soft cheese, perfectly ripe vegetables of choice , top quality butter, sea salt and pepper mill.
Or, whole wheat flatbread and multigrain crackers with Mediterranean spread...greek Israeli Turkish morrocan vegetables and spreads. Maybe serve beer with this menu.
Or, yes, a menu of roasted vegetables and quinoa, served as a salad.