You are exagerating with respect to the He-177, IMO. The early versions were disasterous, but the problems were largely resolved by the time of the He 177 A-5, which of which there were over 800 produced. In OTL He-177s carried 6,000kg bomb loads to London with less than 10% loss rate.
If there is a bomb, the He-177 can deliver it to London.
Clearly, a 4.5 ton warhead rocket is not going to happen. In fact the entire rocket programme will have to be scrapped for the nuclear programme to have any chance. Nazi Germany spent as much of it's GDP on rockets as the Allies spent on Manhatten Project - redirect that money and political energy to the atomic project and, yes you are right, they still won't get it done, probably, but it's going to get a lot further. And as the rockets were militarily useless, you won't damage the defence of the Reich.
Shimbo, I love you like a brother, but I think your idea of the Nazis being able to develop and an deploy an atomic bomb has two major flaws on quick review. These flaws are so great that I think the development and deployment would be impossible.
First, I think you faith in using the He 177 is misplaced. Second, I think getting the Nazis to give up other projects is simply contrary to nature of the Nazi Reich.
As CalBear pointed in another thread, there is a difference between being able to lift an atomic bomb and being able to fly the mission profile to deliver the weapon.
The semi-reliable Wikipedia, where I assume you obtained your ball park figures on the He 177, indicates that He-177 was able to carry 5600 kg of bombs (not 6000 kg) from German airfields to London. This is certainly sufficient payload of a Little Boy type bomb, assuming the Wikipedia is right, as the Little Boy weighed 4400 kg.
The problem is that carrying the bomb to London is different than effectively delivering the bomb. The He 177 appears to lack the ability to climb high enough and fly fast enough to fit the mission profile. (Calbear's above cited post explains what was required.)
The He 177 London mission profiles you cite, assuming we believe the Wikipedia, involved the He 177s climbing to around 23000 feet over Germany. The planes then made long descent to build up speed, attacking London at 14000 feet, and then continuing the descent on way home so the planes would continue to gain speed.
To deliver the A-bomb and survive the blast of the bomb, a plane is needed that can do 300+ mph at 31,000. The He-177 couldn't do that. (The He 177 lacked the exhaust driven turbo-supercharging of the B-29, having just mechanical supercharging, which limited its high altitude performance.)
I also have my doubts about the 10% loss figure you cite for the London raids (which, I presume, also comes from the Wikipedia and were, I also presume, part of Steinbock). I think the actual losses were far higher. I think the 10% represents the losses for planes shot down over England, and not just all planes not returning. I think the actual losses from all causes, such as engine fires, damaged beyond repair, crashed, etc., were much higher. Add to that the planes that turned back, these figures of losses and mission failure become astronomical. For example, the semi-reliable Wikipedia states this:
On the night of February 13, 1944 as part of Operation Steinbock, fourteen He 177 taxied out on a bombing mission, thirteen took off, one suffering a burst tire, eight promptly returned to base with overheating or burning engines. Of the four He 177s which did reach London one was shot down by night fighters.
In the case of an atomic bomb attack the planes would be operating at the very furthest edge of the performance envelope, so reliability would be even lower.
For the B-29s, a more advanced airframe and engine set-up, to reach the performance envelope, they had to be modified extensively. I think this would be impossible for the He-177 to reach anywhere near the performance of the B-29, particularly as to altitude.
Still, you have piqued my curiosity as I respect your opinions, but in this case it seems to go against everything I have I read. I have ordered some books of the He 177. These ought to be in clutches in the next couple of months, so by October or so, I may be able to offer a more definitive opinion.
A greater hurdle for the success of a program as big as the atomic bomb project is the inherent nature of the German economy under the Nazis. The economy, from what I have read, was run as a collection of corrupt fiefdoms--a kakistrocracy. The atomic bomb project would require too many special interests to give up too much to pursue a goal that seems too unobtainable. This alone would prevent the project to proceed in a fashion as rationally as you suggest. Coordination is impossible in Nazi Germany where infighting is the norm, and the most petty and territorial advance. For the Nazis to have an atomic bomb program efficient enough to develop an atomic bomb requires the Nazis to change the entire basis of their political and economic culture, which seems more unlikely than the Nazis overcoming the technical challenges.