Basically, having given you a 30-day notice, you are supposed to be out after 30 days. Even if the landlord was willing to be cooperative, if he accepts rent from you for occupancy after April 8, it would invalidate his 30-day notice, and he would have to start over again.
The basic principle of business says you should go to the landlord and talk with him. Explain the problem, tell him that there is no problem for you to leave after 7 days beyond April 8, and that you have no objection to paying for the extra time you will be in the apartment, either you can pay him AFTER YOU ARE GONE (he needs that) or he can take it from the security deposit. You can show him your new lease (rental agreement) so he can see that you are not going to be there beyond the 7 extra days. Perhaps he will be willing to cooperate, especially if your apartment is not scheduled for repairs right away. Ask if he will simply delay filing for eviction right away.
Alternatively, you could let him file for eviction (be sure to file an answer in court that says the right reasons) and you would have to pay for the filing fees, court costs and legal fees. But you will also have an unlawful detainer filing on your record, and again, be sure that you file an answer in court and it is an answer that says that you are not guilty of unlawful detainer for good reasons, so he cannot get a default judgement after 5 days. I don't recommend this alternative strategy.
Ask your landlord if he would please cooperate, and show him that you will really be out in 7 days, please just hold off on filing the eviction. Be honest and sincere, and admit that it is his choice. If he says no, go to a hotel for 7 days.
