Not at all RajaHarischandra,

Your case seems pretty straightforward. Being on H1B is the best possible situation when you start GC processing. As you need to be maintaining a valid non-immigrant status until your I-485 is approved, H1B is the best back up because of it's dual intent.  Even if there is any complications with your GC processing, you'll be safe and working because of your H1B.

A non profit organization like your University can apply for your H1B anytime and you can start working as soon as it is approved. You can also apply for your wife's dependent visa H4, along with your H1B petition. Her OPT is considered expired as soon as her H4 is approved and she has to stop working. Though she might miss about 2 months of her OPT assuming your H1 starts mid July,  there won't be any concerns about her status at least. As soon as her GC EAD arrives, she can start working again.

April - July is when USCIS is busiest and it'll take 3-4 months to get a decision on your H1B petition during those months. If you file on May, I doubt that you'll get a decision by the time your OPT expires. It's better to file under premium processing. Though it'll cost you $1000 more, you'll get the decision within 15 days of your receipt notice.  

Hope that helps.