Where to start?
Based on this, there wasn't a plane in the Luftwaffe's inventory that could do the job.
Fighter-Interceptors can and do run with the engine at very high revs for the few minutes it takes to fight or climb to altitude. This gives them distinct advantages when compared to bombers which hold the same throttle pos for hours on end! No fighter plane from any Nation had any trouble reaching any even remotely contemporary bomber, ever!
The usable ceiling as defined by carriage of bombs and enough fuel to RTB ( WITH RESERVES!), of Allied bombers ranged from under 20,000' for the British Heavies, to 25-30,000 for the American planes with "Turbo-chargers", ie the B-17 and B-24 to 30-40,000' for the early B-29s which were also required to reduce bomb load and range to meet the higher altitudes. While the performance placards for all of these planes was substantially better than this, those numbers were acquired under test conditions WO load for the Brits! For the British, the published ceiling was how high was the plane when it ran out of fuel, or had some major system freeze up or fail. For the Americans it was that altitude where the rate of climb was 100 feet per minute with bombs and sufficient fuel remaining to land, and hopefully taxi to the hard stand?
This last got so bad that some American planes were REQUIRED to GLIDE for the LAST 200 MILES back to base in order to extend their range and increse ceiling over target! Not Joking! They would start their engines just before entering the landing pattern to have power for the controls! Or dead stick it if they failed math?
As you can see, there is a HUGE disparity between the British, (and German, Italian and Japanese planes too!) and the American planes with Turbos! This is caused by two things; First it is not possible to run any engine at full RPMs/Power for any significant length of time! You will certainly blow up or ruin the engine! It is absolutely imposable! So at reduced RPMs the efficiency of the super charger is reduced by the Square of the difference. IE if the RPMs are at 70%, the the blower can generate 49% of maximum pressure! So in the cruise, all planes with conventional super chargers must fly at lower altitudes. Turbo-chargers on the other hand have less back pressure the higher they go and thus spin faster and make more pressure, regardless of engine RPMs That is the entire difference between the whys of how come American bombers flew higher than their contemporaries.
PS. As an aside, we had full service turbos in 1930,or 31, IIRC! While other Nations, ALL IIRC, tried to make them, they just did not have the materials science that we did and they all failed until well after the war. Do not think that a running jet engine with a life measured in a few dozen hours is the same as a turbo charger with a life measured in hundreds, or later thousands of hours.