Doctrine,doctrine,doctrine and politics.
It was Robert Knauss,a former deputy of Milch at Luft Hansa who in 1933 proposed the development of a "Langstreckench-Grossbomber" to Milch. The paper he delivered is pure Douhet.Knauss' theories were controversial within the Wermacht at the time but were supported by Milch and importantly Walter Wever,the Luftwaffe's first Chief of Staff. It was Wever who famously announced to in a lecture to the German Air War college in 1935 that "the decisive weapon of air warfare is the bomber."
It was Wever's support that led to the issuing by the RLM's "Technische Amt"of a specification for a strategic bomber in 1935. The specification went to Dornier and Junkers. The Do 19 and Ju 89 resulted.
On 3rd June 1936 Wever was killed in a plane crash. He was replaced by Albert Kesselring who had very different ideas about the application of air power. He ordered an immiediate reappraisal of the so called "Ural Bomber" programme. It was abandoned,along with the doctrines of Knauss and Douhet on 29th April 1936.
There were many in the RLM who considered this an error. Most notably Kurt Pflugbeil,the Inspector of Bombers. It was he who eventually pushed through the specification for "Bomber A" in 1936. Heinkel was the only serious contender and was awarded the contract. Work began on project P 1041 in October 1936 with Siegfried and Walter Gunther,working under Heinrich Hertel.
The trials and tribulations of the early development (abandonment of surface evaporation cooling system,extra fuel tanks etc) had already reduced the performance considerably when,in November 1937,Udet suggested to Heinkel that the 177 might not be needed at all. Heinkel threatened to abandon the project entirely to which Udet replied.
"Jeschonnek and the General Staff cannot see a way in which we could use it.Nobody is thinking of a war against England. Goring has had full discussions with the Fuhrer before taking the decision to concentrate all our resources on the twin engined dive bomber.........For the conflicts we are likely to be involved in we only need a medium bomber with a small range and small bomb load. We'll go on developing the He 177 for research purposes. Perhaps we can use it as a long range machine for the Navy,but it must be able to dive or it won't stand a chance."
The He 177 now had to be able to bomb from a 60 degree dive. This led to a whole series of further problems. Heinkel wanted to power the second prototype with four Jumo 211 engines but was turned down by the RLM on the grounds that a normal four engined aircraft cannot dive. Dive bombing capability became something of a fixation for the RLM. When informed of this decision Siegfried Gunter is supposed to have said to Heinkel "they've gone absolutely crazy on dive bombing.It's become a mania."
A four engined design was started by Heinkel under the designation He 179 in 1939 but Udet stopped it on 12th September 1939.
The He 177 was not given a proper production schedule until 1940. According to Heinkel this was in response to Udet's wish to be able to attack the Royal navy at Scapa Flow. He thought destruction of the Home Fleet would force Britain to the negotiating table. Udet rarely comes over as the sharpest tool in the box
Anyways,that's a long way of explaining why no four engined bomber was going to be available in 1941 or at any other time and also giving a bit of background to the doctrinal and political problems which plagued the development of a German strategic bomber force.
An inkling of how the Germans may have used the type can be found in a letter from Jeschonnek to Milch on 28th October 1942.
"the Fuhrer has expressed his opinion concerning the He 177 several times in the last few days,implying that he sets great value on seeing this aircraft operational on the Eastern front as soon as possible,even in its simplest form. He is thinking in terms of nocturnal horizontal attacks against area targets outside the range of our other aircraft."
It was also seen as an escort for U Boats and the Atlantic blockade runners.
There may be problems with your 1941 time frame too. Eight He 177s had been delivered for operational development by Erprobungsstaffel 177 by the end of
August 1942. At this time there were only
four qualified crews.
Although 102 aircraft had been built by late 1942 only 33 had been accepted by the quatermaster-general's office for squadron service.Only two (prototypes V6 and V7) had been delivered to an operational unit,10.(Erg)/KG 40.
Care is needed when drawing conclusions from raw and unqualified figures in Wikipedia type sources.
The four engined concept,now with BMW 801 engines,was resurrected in March 1943 under the initial designation He 177 B,then A-8,possibly to disguise the fact that Heinkel were once again considering four engines.
Cheers
Steve