build a shelf that an ac can sit on and do a cut out of the door for it in the same spot you already have your intake. Mount the shelf on the door so it can sit on the shelf. then you will be fine to exhaust into the same room because the air going back in is cooled and cleaner.
But exhaust back out of the door, instead of breaking through that concrete.... saves tons of bucks, work, and is just as effective.
The reverse system I suggested earlier would have worked as well, but if youre willing to do the AC mounted to the door you'll be fine with that too... just make sure there is still clearance to open the door.
Did you even try rigging up your fan with rubber stretchies?
I was actually going to suggest doing this, especially running 1000w bulbs and one of them in an open hood. It will also serve as a dehumidifier which is going to be essential because cellars are notorious for humidity. Humidity is good for veg but horrible for flowering. You'll have all sorts of problems then. If you do this, go oversized on the AC. I'm sure someone in here can calculate the BTU's needed. Best guess, 8,000 to 10,000 BTUs, but that's just a guess.
So I mentioned that the ac would remove humidity. You'll want to get a humidifier for vegging. Just go to good will and get one for a few bucks. With the ac pulling out the humidity you will have to put a drain on it otherwise it'll just pour water on your floor. When mounting the ac, make sure you tilt it back a little so the water drains at the rear. It might be a little tricky doing the drain piping since the ac will be moving with the door. You may be able to use flexible tubing and just leave some slack for when the door is closed. Mount the ac as high as you can.
Right now is a great time to get used ACs on craigslist.
I really think this is the best approach. However, you're going to have to skip growing in the summer. That ac will be blowing hot air out the back right into a house you'll probably be trying to keep cool.