I would recommend to test in required device instead responsive browser to see if this is happening before investing effort on it
Based upon your requirement I too tried on that while selecting a particular resolution to check the responsiveness in the desktop browser itself it is behaving as you mentioned.
Can you try out once by changing the display settings of your desktop to 1280*720 in the settings->display resolution option you will not get that type of overflow as the dropdown adjusts as per the properties of device.
I had checked with StackOverflow aswell there to mentioned the same thing you can have a look on it aswell.
the below one is the link for it
hope this helps.