Sounds just like the western lawns at Sharp hall. My soil was so bad I completely dug out the borders and replaced with compost, then over the years added extra of home made compost eventually nature takes over, worms and the weather. I dug in a soak away at 2 trouble spots that used to collect water and at the bottom of the soakaway added a pipe and connected it to the drain.
The grass is happy on the same crap soil as it only lives on the very top which gets fertilised and raked and extra seed added each year in the spring.
I think if you go digging where the grass will be seeded then it could end up settling and over time it will be very bumpy, and uneven, I would just spend time not on digging it over but on getting it as flat as possible by slicing of the high sots.