Our Future Home: One step closer. . .one more dilemma

A couple of weeks ago Nic and I submitted an offer on this house and it was quickly accepted. It's 4 bedroom, 2.5 bath with 3,143 square feet. The inspection is FINALLY set for tomorrow (it's bank owned and they were dragging their feet to get the utilities turned on), so we're one more step closer to calling it our very own. Our realtor told us that we probably won't close (the earliest) until April 10th or (the latest) April 20th. Now, here's our dilemma: we asked our current landlord if we could pro-rate our rent for April. He could only charge us the first two weeks of rent and Nic and I would repay him the last two weeks by doing repairs (mostly painting) around the house. We've been good renters and we have never had any problems with our landlord; in fact when we told him that we are looking to buy he said we could work something out since we were more than likely be out before our contract runs but now he's singing a different tune. He told us that if we stay for anytime in April that we would have to pay the FULL months rent, unless we are out by April 1st because he had some people that we're REALLY interested in the property. That only gives a week and a half to finish packing and getting the house cleaned and then we would have to find a place that could accomodate us, our stuff AND our cats. I wasn't stressed before, but now I am. Maybe, I'll call our land lord and negotiate with him. AARRRGGHH!!! I'm so frustrated! But everything will work out. . . . .right?