Pretty good list. I think Mandlikova (4) would be in the top group. I fully expect Swiatek to reach a higher level, but for now.
My sense is that Barty belongs to, at least, the second-highest group, and not sure if Kvitova has had a much better career than Muguruza - both very streaky. Virginia Wade also has three, and is maybe a third-tier player.
Quickly without poring over the records:
Highest Tier: Swiatek, Davenport, Mandlikova, Sanchez-Vicario, Clijsters
Second Tier: Barty, Kerber
Third: Osaka (I know she hasn't done that much outside those 4 majors, but), Wade, Azarenka, Capriati, Halep
Fourth: Kvitova, Mugu, Pierce
I like quite a bit of these but have got some disagreements (and I did go over the records so no shame in your effort which was very good).
The big disagreement is Kerber in the second tier, one above Capriati and Osaka.
Both Kerber and Capriati have 3 slams, both won 14 titles. Things get different when you remember Capriati won Olympic gold (over Graf!) as well as two 1000 titles. Kerber only got Silver (losing to Puig) and has never won a 1000 title. Capriarti is above or the very least on the same tier as Kerber. Angie is not better in any metric from what I see.
Also, Osaka, she may only have 7 titles but 4 are slams and she also won two WTA 1000 titles including Indian Wells. Kerber, not one 1000 title. Does Kerber winning 7 more titles (none of which are 1000 level) make her better than Osaka despite Naomi having one more slam and 2 1000 titles? I say no.
Also, not getting the Kvitova underrating!
Let's have a look at some stats for the 4 active ladies on 2 slams (Kvitova, Halep, Muguruza and Azarenka)
Petra has the second most WTA titles of all active players with 30. Halep is at 24, Azarenka is at 21, Muguruza is only at 10.
Kvitova has 9 WTA1000 titles, the same as Halep. Azarenka has 10. Muguruza has 3.
Kvitova and Muguruza both also have a WTA Year end championship, Halep and Azarenka do not.
Kvitova and Azarenka both have an Olympic Bronze. Halep and Muguruza have no medal.
Azarenka and Kvitova's 2 slams were both at the same slam while Halep and Muguruza each won a Wimbledon and French Open.
Azarenka has 3 extra slam runner ups, Kvitova has 1, Halep has 3 and Muguruza has 2.
As for Pierce who also won 2 slams, both were different, she made 4 other finals, won 18 titles including 5 WTA1000s so i'd bump her up to Third too as she's clear of Muguruza.
I'd probably go:
Highest Tier: Swiatek, Davenport, Mandlikova, Sanchez-Vicario, Clijsters
Second Tier: Barty, Capriati
Third: Osaka, Kerber, Wade, Azarenka, Capriati, Halep, Kvitova, Pierce
Fourth: Muguruza