In Rahman v. Napolitano, http://www.ca6.uscourts.gov/opinions.pdf/10a0419n-06.pdf (unpublished), the court was confronted with an appeal from the denial of a petition for a hearing on a delayed naturalization application, pursuant to 1447(b).
The facts are somewhat complicated. The LPR applied for naturalization. While her application was pending, she pleaded guilty to a federal crime and was placed in removal proceedings. In addition to the conviction, there was apparently a previously undisclosed in absentia order. After the initiation of the removal proceedings, she filed the 1447(b) action in district court. Between the filing and proper service on the government, the USCIS denied the naturalization application because of the pending removal proceedings, and the failure to disclose the criminal activity and prior removal order.
Following Zayed v. U.S., 368 F.3d 902 (6th Cir. 2004), the court found that the bar on granting naturalization applications for LPRs in removal proceedings, 1429, trumps 1447(b). While the district court has jurisdiction under 1447(b) to consider the matter, 1429 restricts the available remedies. The court can only grant what the AG would be and if the AG is prohibited from granting naturalization because of the pending removal proceedings, so to is the court.
Although it did not decide the matter, the court noted that the weight of the authority seems to support the view that 1447(b) grants the court exclusive authority to decide a naturalization application, so the USCIS could not deny it once jurisdiction vests with the district court. The court did not have to reach this question because of the reach of 1429.