About 2yrs ago I was involved in a horrendous J1 visa/IAP-66 mix-up (through no fault of my own) the end result was that I 'withdrew my application for admission' (to avoid being formally deported.) This was at JFK and I still remember being marched back onto the plane while my (american) girlfriend ran through security in tears to see me being taken down the jetway.
Now barred from visa waiver I applied for a B1 and started travelling back and forth to the states, always being placed in the INS office and given an interview. Last Xmas I had my passport stolen in Pittsburgh and travelled home on an emergency one.
If you have had your passport stolen do not forget to write a letter informing the INS of the loss of your I-94/I-94W!!!! I was told be an INS officer that this creates all sorts of difficulties.
After reapplying for a passport/B1 visa in the UK I was a bundle of nerves when I last flew LGW-CLT.
I got to the INS line and was let in with barely a 2nd look, despite being on a different passport number, a previouslu lost I-94 etc. A breeze, I was through INS in minutes.
IMO the amount of trouble you will receive depends on two factors.
1)Which airport you fly to. I have heard multiple horror stories regarding JFK/LAX/PHL. Flying to CLT or PIT (with far fewer intl flights) is always a lot less stresful for me.
2)Which INS officer you end up being processed by. They have the power to put you through some serious grillings. But, I've always told the truth, called them sir/officer/ma'am and been ultra polite.
I would make sure you have time for any connection, in case you end up being given an INS interview.
Ultimatley, people have passports stolen all the time and you aren't the first. As long as your papers are in order you should be just fine.
Hope this puts your mind at ease and the very best of luck to you....