OK, let's try this one more time. I forgot my pendrive at my work, so I can't cite specific paragraphs and cases, but I'll try my best to make my point without these.
The naturalization process has several steps, one follows the previous and you can't change the order of these steps.
After you apply for naturalization, USCIS initiates an investigation, which contains also the name check where most of us got stuck. There is no time limit prescribed in any of the statues or regulations, how much time they can take to complete this investigation. After this is done, they will examine the applicant, this is the interview. (USCIS usually disputes this and tries, in most of the cases unsuccessfully, to show that the examination is a process and the name check is part of it). From the day when USICS interviewed the applicant, 1447(b) kicks in and the 120 day clock start ticking. If they don't adjudicate the application, applicant can file a complaint with the district court and ask for a hearing. The court can conduct a hearing and decide the matter or can remand the matter to the Service with specific instructions.
So UNTIL the applicant didn't have his/her interview, there is no time limit for USCIS how long they can take to call you for the interview. In these cases only the mandamus+APA can help, but it is a lot more difficult case, because you have to prove that USCIS owes you a non discretionary duty to adjudicate your case without an unreasonable delay. What is unreasonable, it is discretionary and will depend on the court.
If you are lucky and you already had your interview, you don't need the mandamus because of 1447(b). The first thing is to fight the USCIS twisted interpretation of the word "examination" (they will claim that the name check is part of it so the 120 day clock didn't even start) to prove that the court has subject matter jurisdiction. But this is only half of the story, because no court will determine the matter (i.e., grant you citizenship) without the finished background check. So the judge will elect the second option conferred by 1447(b): to remand the case back to the Service. And here is the second critical issue: to convince the judge to order certain actions in certain timeframe. Otherways, if the remand is like: "USCIS should adjudicate application immediately after the FBI finishes the background check", this will not solve your problem.
You are correct when you put the emphasis on the word "shall" in your citation from 335.3. But only AFTER applicant has complied with all requirements for naturalization, which include also the "full criminal background check". The name check is part of it, so no name check completed, no adjudication. I wonder why so many people left out FBI from their defendants' list... Remeber: if the sequence is A then B then C..., you can't ask C before A and B is not finished. If you don't sue the agency responsible for B, the court can't compel them to complete B and if the court compels the agency responsible for C, without B being completed, the only way to comply with the court order is to deny the application, because the law mandated B before C.
Finally, you are right. "it is the sense of the Congress..." means that Congress recommends this timeframe but it is not mandatory. If this would be mandatory, all these cases (N-400, I-485) would be trivial. They didn't adjudicate in 180 days, so they broke the law and you can sue them. As you see from this forum and many, many WOM and 1447(b) cases, life is more complicated. Absolutely none of the lawsuits were won because this "it is the sense of the Congress...180 days..."
I hope that this helps.