You should always consider the reduced performance applicable to an engine out. Regardless of the runway or surrounding terrain.
You're legal to depart under the situation given. Accelerate stop asumes an engine failure at V1. A failure or a reason to stop that occurs sooner than V1 means a shorter actual accelerate-stop distance.
Convsersely, if it's safety you'e concerned about, most likely your accelerate-go distance will be longer, especially for the aircraft you've indicated. If you lose an engine and attempt to go, you're out of luck if you've predicated on just meeting accelerate-stop criteria. If you're going to seriously consider reduced climb performance based on an engine-out, then you MUST consider accelerate-go criteria...after all, if you're going to be climbing on one engine, then obviously you are not stopping.
The truth is that many times you may be faced with situations operationally in which you don't have 12,000' of runway to use, and you won't have the performance to meet all of the Part 25 criteria you're accustomed to meeting under Part 121. Not gonna happen. You then need decide if you're going to do the job, or not.
I routinely operate in one of my jobs in situations that use all the runway, or even a little more in some cases. V1 occurs as you taxi onto the runway...after that, you're going. Period. Lose an engine, and life gets tough, no matter how you slice it. That's part of the job. You must decide what you can and cannot accept, and live within those means.
You indicated that "waiting for temperature to drop is not an option." It's always an option. I've been in situations in which the passenger arrived, and said he wanted to depart at eleven o' clock, and by the way, we'll be bringing two extra people, and...so on. Running performance in that airplane, I looked at the weather, the rate at which it was warming up and told the passenger fine, but you won't be departing at eleven o clock. It's going to be after six tonight when the temperature is less. Or you can go now. What will it be?
If the charter is predicated on a specific time and can't go at any other time, and you can't live or operate with the temperature, then clearly you can't take the flight.
Under Part 135, you needn't observe accelerate stop distance in a Part 23 airplane...but you do need to observe takeoff distance.
Part of the utility of a King Air is the ability to go into small places and stop in short distances, and then come back out of them. That's part of the reason it's being used. To be employed in an airplane that is featured because of these capabilities, you need to be able and willing to take advantage of them.
You also need to be able and willing to set your own limitations, and not budge from them. More than a few times I have stopped short of a destination in a light airplane to get a hotel, due to weather or other conditions that were beyond my own personal limitations set. I won't go beyond them. If an employer doesn't like it, he can find a new pilot. I've refused to fly aircraft, and refused trips, even under heavy pressure from employers, clients, etc. I once turned back a flight with a medical team on board, enroute to pick up a waiting heart during the flight as conditions changed. I've refused to deliver retardant to a fire, or to put the airplane into situations when clients, employers, agencies, or others demanded it be put, and I will do so again. Don't you do any less.
Do the math before the employer accepts the flight. Tell the employer you can't do it. Tell the employer that it's beyond the performance limitations of the airplane. Yes, it can be done when everything is working, but we don't plan flights with the idea that everything will be working. We plan for emergencies, failures, etc. That's what we do. Carrying passengers off of a field means that you needn't take chances.
You indicated that reducing takeoff weight won't change your aircraft performance. Of course it will. Less weight reduces accelerate stop distances, takeoff distances, accelerate-go distances, and will ultimately reduce balanced field length where required or available. You may not see an appreciable distance change with a few pounds difference, but reduce that weight by a thousand pounds, and you'll see a difference.