The '44s are not grade scarce, they are harder to find in any grade.
There is no way that anywhere near 1.3 million were put into circulation.
If you look at their Canadian cousins you'll see that MS63 war year coins are all apparently scarcer than their 1938 counterparts, despite much higher mintages. I'm sure that at both the British and Canadian mint during the war years quality of coins took a back seat to quality of ammunition products.
The only outlier is the '42 which at 1 in 7 isn't unusual.
"Dipping" is not considered cleaning...
-from PCGS website