Let's clarify something first. Is she on a non b visa( 90 days from date of entry and it's a sticker NOT a stamp) or is she now on extension of stay ( one year extension and it's an inked stamp NOT a sticker)?
If she's on the initial 90 day non b (sticker) then she doesn't have to do anything. She can, if she wanted, stay untill August 22nd. As she leaves soon, then this visa (without a re entry permit) simply ends right there
Speak to your immigration officer. Explain the circumstances to see if they can accommodate your request. Some are on a power trip but most are pretty reasonable. Get your wife to do the talking.
You've got plenty of time. There are no public holidays around that time. Do as Tod suggests and get hold of the list of requirements from your immigration office. Take your wife and write down what else they want what isn't on the list. Make sure your landlord has done the TM 30 for you , check that he's done it and get him to contact immigration that it's done properly. Ask if you can make an appointment for the 5th May . When you apply your wife will need to be there also. Write off the whole day for the process and expect to have something missing and have to go back another day.