Having had a "good copy" of a 5D3, I hate to say it, but indoors at 6,400 ISO I think your expectations are well ....
A little optimistic.
I also think for folks to help you ... Well I personally would want to know ss, aperture, iso and the lens you used.
For the kind of quality I Wanted - ISO 800 max, or at a push ISO 1600. But then I am picky
but also very realistic.
I generally tried to stick at ISO 160, if it demanded more light then went the flash route. Or at least stuck between 160 and 400.
Yes, I Realise thats awfully restrictive, just saying it as I found it.
If you want to go over that, and still get those ... what I call wonderful transparency like, glossy black and whites then you will have to get awfully good at post processing.
Look at posts from a guy called Teamspeed, he seems to extract magic out of these Canon cameras.
My friend has a Nikon D810 .... And again I hate to say it, but that Sony sensor seems more in line with what you are wanting.
I am sure loads of folks will disagree with me. My response would be ... OK post some utterly stunning ISO 6400 images and tell me how you did it!
Canon EOS 5DS R, Canon EF 70-200 F2.8 L Mk II IS USM, Canon EF 70-300 F4-5.6 L IS USM, EF 40mm F2.8 STM , RC6 Remote. Canon STE-3 Radio Flash Controller, Canon 600 EX RT x4 , YN 560 MkII x2 ; Bowens GM500PRO x4 , Bowens Remote Control. Bowens Pulsar TX, RX Radio Transmitter and Reciever Cards. Bowens Constant 530 Streamlights 600w x 4 Sold EOS 5D Mk III, 7D, EF 50mm F1.8, 430 EX Mk II, Bowens GM500Rs x4