Okay, so there are several misconceptions at play here.

##1: 'Germany chose to give France an extra 8 months.'

In Hitler's mind, nothing could have been further from the truth. Indeed, in his Führer Directive No. 6 of 9 October 1939, directions were given that "an offensive will be planned on the northern flank of the Western Front, through Luxembourg, Belgium, and Holland. This offensive must be launched at the earliest possible moment and in greatest possible strength". This was indeed further elaboration on an even earlier statement to the German generals on 27 September, in which Hitler stressed his belief that a rapid opening of hostilities in the west would only be favorable to Germany. So, in a way, Hitler agreed with your initial assumption that an immediate continuation of the war would have been the most natural choice. This assumption has been judged wrong by most military historians, but Hitler certainly did not initially have a seven month delay on his mind.

On 25 November 1939, Hitler further specified that he believed this attack to be possible "within three weeks". Now, Hitler's paranoia about time might have been just that - paranoia -, but it is absolutely true that Germany was low on vital resources, and had essentially no reserves of materials such as nickel, tin, tungsten, molybdenum, chrome, beryllium, platinum, or bauxite even in late 1939 (resource shortages would remain a continuing theme in Germany's experience with warfare throughout World War II).

But you know who was convinced that Hitler was mistaken (if not insane) for his plans of rapidity? The German generals. Stülpnagel estimated in a late 1939 memorandum that no promising breakthrough could be achieved against Franco-Belgian forces before early 1942 (!), and although Hitler insisted on the general idea of an immediate attack, he allowed the date of attack to be delayed at least 29 times (!), before ultimately settling on 10 May 1940.

##2: 'The Manstein Plan was not fully developed.'

Not only was the Manstein Plan not fully developed, the Germans had not yet adopted it -- it wasn't developed at all, except perhaps in Manstein's mind. Erich von Manstein's fame as "Hitler's greatest general" is a postwar creation, and he belonged to the niche of commanders (along with, most notably, Rommel and Guderian) that emerged from initially junior ranks of the generalcy in the early phases of the war with conceptions of their beloved daredevil panzer dashes that so appealed not only to their new generation of officers (those who would have been at most junior lieutenants during World War I), but also - decisively - to Hitler's conceptions of a knockout blow style campaign.

But initally, the plans on which Hitler and the superior generals (among which none of the aforementioned daredevil panzer leaders were yet to be found) initially based their military operations initially appeared to be, to use internet lingo, "Schlieffen 2 Electric Boogaloo" (even though a more detailed analysis of course reveals stark differences). The plans conceived a stationary left flank along the Franco-German border and a swinging hammer of mobile forces to advance on the right flank through Belgium (as well as, this time, the Netherlands) into France. Hitler, over the course of his initial considerations, eventually landed at a plan which would have required three main columns of attack - one via Brussels, one via Liege, one via Sedan... three Schwerpunkts at once? Such an approach defied all German military orthodoxy.

But Hitler remained with the idea until a fateful moment in January 1940, when a German plane carrying secret plans that the officers aboard only managed to partially destroy crashlanded in neutral Belgium in the infamous "Mechelen Incident". The Germans feared that their precious plans had been lost to the Allies, Hitler went on one of his trademark tirades, and the plan remained... initially unchanged - no serious alternative had yet been presented. The chief of staff working under general Gerd von Rundstedt aimed to change that.

Erich von Manstein had served satisfyingly under Rundstedt in Poland, and was now to continue his previous assignment as Rundstedt's chief of staff. When he received the initial draft of the initial plan with its heavily reinforced right wing swing into Belgium, he was concerned over several weakspots. Firstly, the plan would inevitably result in Schwerpunkt clashing Schwerpunkt, as the Allies would of course reinforce their left and advance out of France into Belgium to meet the Germans as soon as the operations began. And even if the Allies would be beaten back (which was by no means certain considering the more than respectable military strength assembled by Britain and France), they might just repeat 1914, reassemble their lines in the riverlands of northeastern France, and beat the Germans on French soil as they had done in 1918. Additionally, the German swing around the right would invite concentrated Allied counterpunches in the center (as had happened in 1914), putting the Germans at threat of encirclement and forcing withdrawal (as had happened in 1914).

Instead, Manstein proposed his sickle cut: a reasonably strong right would advance into Belgium and the Netherlands to bait the Allies into meeting them in Belgium, then a super-reinforced German center would break through the Ardennes (generally thought to be unfavorable for armored formations) in southern Belgium and Luxembourg, cross the Meuse at Sedan and race to the channel coast at the Somme estuary to cut the Allied armies off in the north.

Manstein initially met considerable resistance to his plan. Halder dismissed it as an egocentric attempt to give Manstein's own army group (the one in the center) more importance, Brauchitsch blamed a lack of available forces as his grounds of refusal. Halder was annoyed enough to promote Manstein from army group chief of staff to the commander of an army corps (technically a superior post, but much less important in terms of strategic and operational planning), and assigned Manstein to the minor 38th Army Corps to neutralize him. It was some of Manstein's previous subordinates who forwarded the plan 'via the backdoor' to Hitler, who immediately saw himself justified in his previous own proposal of attacking via Sedan (even though of course Hitler's plan included two additional Schwerpunkts at Liege that Manstein's version lacked). After a meeting with Manstein in Berlin on 17 February, Hitler was convinced, and at long last adopted the "sickle cut" idea, as it is now known.

The Schwerpunkt of the attack to be mounted across the territory of Belgium and Luxembourg is south of the Liège-Charleroi line.

• Fourth deployment directive for Case Yellow, 24 February 1940

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For further reading, I recommend Karl-Heinz Frieser's "The Blitzkrieg Legend", initially published in the original German in 1996 and published in its English translation in 2005. Frieser's work remains the central standard work (introducing several exciting revisions on previously established orthodoxy of the campaign and the "Blitzkrieg" concept in general) on the 1940 Western Campaign's military history and background, and is recommended as such by military historian Robert M. Citino in his contribution to "A Companion to World War II", 2013.