That's a very wiiiiiide game.
39 views and no answer isn't really something to comment on. Those people that looked at the post may have been looking to see if you had the same problem as them and hoping for an answer too. Or it could be that the people trying to figure out your issue just haven't solved it yet. Patience is a pretty sweet thing to practice. Almost all problems on this forum get answered before too long, just gotta wait sometimes while folks brainstorm.
As for your problem... unfortunately, screen size isn't something that's easily patched in if you've got things like statically positioned HUD elements to contend with. In all likelihood you will in fact have to go back and edit all the positions. Some things to also consider are what you want in your resolution changes. Do you want only one aspect ratio and have the "gaps" to be covered up so you only see your ratio? Or do you want the player's viewport to expand or decrease depending on their screen resolution? Are you planning on adding zooming or other camera tricks? I'm sure the other more experienced Construct guys could think of more scenarios, but the first thing you'd need to know is what you even want.
Your resolution is really bizarre. Is there a purpose behind it?
Also, when seeking help, it's recommended that you also leave a link to your game's cap file, preferably a Dropbox link. That will help with solving any issues or making any suggestions immensely, since all we really have to go on is you say your game screen is 1680x105 and that you'd rather not have to recalculate object positions. So post a link to your cap, and maybe I can see if my method for resolutions would help you out.