Pockets.
We used to go to the parks bagless back when bag searches were slow.
If we trended to bringing a bag, it was more in summer, for water and rain ponchos.
In winter, we tend to wear hoodies, and just unzip them in the afternoon, maybe tie around our waste. (though really cold days require a little extra).
At Universal, the wands are a bit of pain to carry. For the wand, we do have a mini backpack- but we tend to only bring the wand to the parks for a few hours in the evening (paired w/visit to the car or hotel room).
One thing that makes it hard to go bagless is if one's family has to carry emergency meds and/or need something like sunglasses/liquids/other item for medical reasons. Personally, I find sunglasses are more hassle than help in the theme parks. After breaking a few pairs, I gave up. For sunscreen, we only carry the tiny Chapstick style. (and use bigger cans that stay in the hotel)
For the parks, we have jackets that are called foldable parkas. They are meant more for wind than heavy downpours, so they won't hold up to WDW's summer storms, but other times of year they work. They fold down into the pocket of the jacket. Just as you say you roll yours, I think. Otherwise, we carry plastic ponchos, and those will fit in any back pocket. If the forecast really looked to be bad all week, I might pack some of the heavier ponchos. which might = carrying a bag)
Another small necessity at WDW these days is a small portable charging bank.
We dislike having to deal with a backpack all day, so we try to avoid them, and carry the smallest bag possible. At Universal, bags means having to use the ride lockers, so better if that can be avoided.
If I go to Sea World Orlando, I might try the one liter since their policy doesn't specify size. 
