I would say that your AFM runway numbers are derived only for a specific Density altitude and prescribe how much runway the aircraft would need to take off under those conditions considering accelerate stop/go distance, balance field length etc.
An AFM can give you climb limit weights as a guideline but can not account for every airports unique obstacles. This is why we use runway analysis like APG to derive takeoff weights in the real world. The computer runway analysis will be limiting in this scenario for part 135 and 121 because it DOES take into account the surveyed plane surrounding the specific airport. Every takeoff must be assumed to have the OEI performance associated with that airport.
The computer analysis or APG or whatever service you use will offer weights that are higher provided you use the OEI DP that would be provided SHOULD you bag one on departure. These weights will give you TERPS obstacle clearance ability for you particular aircraft. That being said, if its VMC, then you can just climb to 1500 feet AGL or the prescribed Obstacle Clearance Altitude and then see and avoid to go run your checklists and return to the airport. VMC does not exclude you from having to have the single engine performance required by TERPS for obstacle clearance. It just allows you to see and avoid and possibly just stay in the traffic pattern to return to the airport at pilots discretion. I hope this helps or at least doesnt make it more confusing
In short; yes you must adhere to the limiting weight, no you do not have to follow the OEI ODP in the event of an engine failure in VMC. And I dont know the exact place where it states all of this because I dont have a TERPS or FAR with me right now but its all in there somewhere : )
I fly part 91 and we still use APG because I need to prove to myself that we can maintain obstacle clearance, however I dont think it is required.