The Imperial War Cabinet doesn't seem to have been so sure of that.
According to Harold I Nelson Land and Power Ch 2 "Concurrently, however, a grave manpower situation faced the Imperial ministers. According to information before them, by December 1919 British divisions in France would fall to 36 compared to 59 in August 1918. French divisions would total 65, American 112 and German 170. This weakness in manpower foreshadowed a diminution of British military power and diplomatic influence on the Continent."
I suppose the ministers may have overrated German strength, and maybe American, but presumably they knew roughly what they themselves had or could expect to have.
Your estimates are for the end of 1919, not 1918 or 1917. This estimate is after the German 1918 offensives and right before the Hundred days, which was predicted to be bloodier than it actually was. Your prediction also includes the planned 1919 offensive, which predicted the Germans remaining in the field supported by the Hindenburg line or at least something similar, as well as an intact, dedicated German force that still fought with the power of late 1917, early 1918. None of this indicates that the Germans would have been far less qualitatively sound than the Brits, as they maintained much higher physical standards than the French or Germans by this point. Also, remember that the Australians have not even introduced conscription yet, nor does this reflect the manpower of India or the troops freed up when the Middle East theater wrapped up. This prediction does not seem to think that the war will have ended on any front.
According to Keegan's one volume work on WW1, he mentions LG holding back several hundred thousand men from the army before the German offensives in 1918 as a result of the bloodletting of 1917 and to prevent Haig from launching another Ypres offensive. This manpower was released after the Germans attacked, and was used up in subsequent fighting. Without American intervention, you've postulated that the Germans would not launch their 'peace offensives', which means the British manpower would not be eaten up.
Beyond this is Germany's allies. While Germany would have been able to stick it out, her allies were collapsing. I doubt AH, Bulgaria, or the Ottomans would have been able to last anywhere near as long, even without offensives knocking them out. Germany hoarded any imports that arrived, to the detriment of her allies, which left them out in the cold so to speak, as their industries and food supplies were collapsing in 1918.