What about thin gray lines? You could also possibly outline the outline. For example, let's say a character's outline is 2 pixels wide and it's part of their frame. Start on pixel 3 and 4, "expanding" the outline in a way to compensate for the style? Maybe the characters could all be different monochrome colors, like one is all dark-gray, another is dark blue, etc?
Another option is to settle for different body language. Hugging isn't visually readable without outlines, or lighting (but I think one or two hugging "poses" could work, strictly from the side? Depends on which characters as they all have different shapes), but hand-holding is very readable.
With styles like these, I've noticed they get the emotional, intimate scenes across by being very atmospheric. As you've noted, there are limitations to certain styles, especially when it comes to body language, but the atmosphere can help do a lot of the work, just like music.
The main character of Jeff Smith's Bone comic has a simple style, albeit it's much easier to see what's going on because of the style, and he hands hands,.
Adorable art, by the way!