Industrial targets were hit many times. From the aero engine factories, tank/AFV factories and indeed oil targets.
Just because there was no great accuracy, bombers (and bombs) still came in. Further, there is nothing to prevent greater effort in training and developing of optical and electronics aids. Even the humble flares as used by FAA would've been a boon for the night bombing, but problem with that idea was that it was developed in the late 1930s by an entity that was not true & pure RAF.
AFAIU the decision to focus on bombing cities ('dehousing') was made because they came to the conclusion that a target smaller than a city was very unlikely to be hit at night, given the technology available at the time. Sending lots of men to their deaths just to bomb some cows in a field wasn't seen as a good trade. Technology did improve rapidly, with the radio navigation (e.g. "battle of the beams during the BoB"), and starting in beginning of 1943 bombing radar (H2S) started to enter service. Which I guess was kind of a game changer, allowing bombing at night or through cloud cover during the day, as accurately as day bombing on a clear day (?)(not that daylight high altitude bombing was very accurate to begin with, but at least it's something).
Unless WAllies are not deep in France by, say, August-September of 1943, there is no way that the war can end by May of 1944. Especially with LW being with full stocks of fuel and their aircraft manned with the pilots that have full set of flying hours as the WAllied pilots, and not just a half - or worse - as it was the case historically.
The historical Normandy landings were supported by hordes of bombers and light bombers as-is.
Yeah. That's kind of a big issue with these "end the war sooner by better air strategy allowing an earlier Normandy invasion" what-if scenarios. If you want to do the invasion during the summer, well maybe you could pull it in from the historical by a month or so. But an invasion during the summer 1943, well a rather huge number of things need to be in place to make that a possibility (win the battle of the Atlantic, ferry a huge number of men and material over to the UK, train the men, beat the LW, etc.). It seems quite unlikely that everything would be in place so that an invasion is possible in the summer (or even early autumn) 1943.