Bicker, I asked my Trusts and Estates attorney about this yesterday and meant to post to you.
NJ used to have a Notice to Creditors publication requirement but that is no longer the case. As the executor, you are required to pay all known debts of the deceased. Since you are reasonably aware of your mother's debts and would know if she had a credit card, car loan, mortgage, personal loan, etc, you probably are aware of the known debts. This would include any dr bills that might be floating around.
The PP who said that estates do not stay open forever is correct. Because you will have to file tax returns for the estate, you eventually want it closed. If you feel that you have handled all known debts, all have been paid, there is nothing outstanding, etc., then you should make any disbursements of remaining funds to the beneficiaries and have the estate closed and file the final return.
If, however, a creditor turns up, they have a statute of limitations on how long they can wait to go after the estate for money. If the estate is closed and all funds disbursed, there is the possibility of them going after the beneficiaries, but if the amount is small (and unless we're talking a hospital bill of thousands or some other large amount) they probably won't. My attorney didn't know offhand the statute but if you want me to check further I can.
Hopefully you can get this done quickly and easily. I'm sorry that you are having issues with your current attorney. I would always recommend our firm, but again, there are always costs involved and since you're already paid to someone else, you should just finish and get done with it.
Oh, and I asked her if you should send the letters and she didn't think that it was necessary. You probably have notified all possible creditors of her death (and my attorney said that these kinds of creditor routinely troll the death records and find out immediately that someone has died so they get their claim in) so I wouldn't bother with the letters.
Hope this helps.
Oh, and in case you don't remember me, I live in NJ in the same neighborhood as your brother (I think we had some PM conversations about that!).