Well part of your crew briefing would include your plans for immediate (smoke/fire etc) return and non-vital issues (typically following the SID to a suitable point to hold or OEIO procedure). This would be a discussion on the ground to prevent rushed decisions.
Numerous factor dictate your decision (ie weather, terrain, performance, maintenance locations, length of flight, takeoff alternates etc).
If time allows, any of the models above will do as they are all structured to help prevent the issue you stated in your initial post.
Also, unless you don't want/need ATC jabbering away in your ear while you handle some post-V1 issue, then make use of CRM and declare something, you can always downgrade later on and it helps them to know your intentions (as briefed). So even if you are too busy to get drawn in with them, at least say something like "Mayday mayday mayday, G-ABCD, engine fire, climbing straight ahead, Standby"