Make 2 scenes, one with the webcam scaled small and the other big.
Try setting up hotkeys, they work wonders.
I use a lot of my "F Keys" to change scenes as well as a lot of my Number Pad Keys to.
Also...
If you basically use the same overlay for each game... just set obs game capture to capture any fullscreen game.
Settings that will also detect games that are running in windowed borderless and/or windowed fullscreen.
PS - A lot of scenes you say... I have some scenes that have 5+ scenes within one scene. I have almost 25 scenes now and use 99% of them every time I stream. You can never have too many scenes to the point that of which you wouldn't mind making one more. (You can Copy Scenes BTW, Just sayin.)
Sometimes it takes a few seconds for obs to recognize the game, about 5 seconds or so it normally what it takes for me. Just gotta have obs running and have the game focused, it should detect it after a few seconds or so.
Depends on how many scenes you use during your streams/recording. I have about 25 scenes, but I only have hot keys set to switch between about 5 scenes, the other hotkeys I use are to mute audio and stuff like that.
Example... (My Settings)
F6 Changes to my Fullscreen Webcam Scene
F7 Changes to my BRB Scene
F8 Changes to my InGame Scene
F9 Changes to my Desktop Scene
F10 Mutes my Mic Audio Channel
F11 Mutes my Music Audio Channel
etc......
Anyways... yeah I gotta go to sleep, my head is starting to hurt, been away almost 48 hours now.