Hey Squid-
I have exactly the same issues. I can't leave the closet door open more than about 3 hrs a day. Here are some things I am doing and considering.
If you really can't bring yourself to cutting a hole in the closet ceiling, this may provide a solution. You would still need to exhaust this unit out the window, but it comes with a fairly stealthy kit to do so. No law against having a portable ac unit, right?
http://www.homedepot.com/Appliances-Heating-Cooling-Air-Quality-Air-Conditioners-Portable-Air-Conditioners/h_d1/N-5yc1vZbv64/R-202051352/h_d2/ProductDisplay?catalogId=10053&langId=-1&storeId=10051
Check out the user manual for installation and any other concerns you may have...
http://www.lg.com/us/support-product/lg-LP0910WNR#
Doing this won't allow you to close the closet door, so it won't ever be stealthy. I think it will offset the heat build up from the tent exhaust.
If you are going to stay in that rented place for another year, you should consider exhausting into the attic. It's really pretty simple. Go to the hardware store and buy a hole saw, attach to your drill and bada bing, bada boom.
I put mine directly behind the light fixture and saved the hole cut-out so I can replace it later. It will need a little spackle and spray texture and paint, but it should be unnoticeable.
Failing that, I thought I might put in a small fluorescent light fixture in the closet that would cover the hole. This still won't enable you to close the closet door because you still need a supply of cool, fresh air. To address that, I am installing an AC vent in the closet. It's also pretty easy to do, just a pain in the ass.
If you decide to try the ducting and venting route, PM me and I'll try to walk you through it.
I think it will be the only way to go stealth in our situation.
If you choose a portable AC unit, please let me know how that works out.