Offloading the social deduction element to NPCs could be a really interesting solution to that discomfort. You could turn to (non-social) deduction games for inspiration; Clue (aka Cluedo) is the big one, but I really enjoy more modern takes on it like Herbalism and The Search for Planet X.
Or, you could set up those NPCs in a GM situation, so that the social deduction is filtered through the GM's discretion. Maybe you'd get more distance from lying right to each other if it's just one of the characters someone is playing that's lying?