If i remember correctly, the Multigrade II filters had to be used with the Multigrade II paper, which was replaced with the Multigrade III and later IV paper some thirty years ago. It came with some kind of calculator, because you had to change the exposure time of the paper when changing grades. With the introduction of the Multigrade III paper, a new filterset was introduced where you only had to change the exposure time when switching grades between 3.5 and 4. A second reason to replace the old set is that filters tend to bleach, especially the higher grades. And as your current set should be at least 30 years old...
But why not use the Kodak filter set on the Ilford paper? To my understanding they were pretty much interchangable, with only minor differences between the sets.