From the comments and tests I'e seen from real 'experts', the Nikon D500 is now the best APS-C camera ever built; the autofocusing system is now Generation FIVE...for birds in flight, football, action sports, etc.., the Nikon D500 is considered third best overall, behind the Canon 1DX Mark II, and the Nikon D5. In tests, the D500 scores ahead of the Canon 7D Mark II, Nikon D7200, and all other APS-C cameras across 100-shot strings, the D500 can hit focus far better than all earlier, or current cameras, except the Canon 1DX MkII or the Nikon D5. In terms of the way the D500 was designed and built, the body layout and controls, and the articulated screen, the buffer depth, the write-speed, the AF system.metering, light flicjer control for indoor sports, everything...the D500 is the best $1999 camera ever made. Period. For 'action work', most camera reviewers are calling the D500 the best value ever offered. Nikon has been making mass-market D-SLR cameras since late 1998. There is a real reason the Fifth Generation means something very significant. Read the reviewers who have tested the D500 (Tony Northrup, Thom Hogan, FroKnowsPhoto, The Angry Photographer,Matt Granger, etc.).
I understand what you mean about the D750: it is and always was built on a consumer-type chassis and viewfinder system; when it was introduced, it was VERY well-reviewed. it has a fine, fine sensor in it, but I know what you mean--it is a "consumer body" camera. I am used to the D1,D1h,D2x,and D3x flagship Nikons, but have also owned or used D70,D40, Fuji S1,S2,S5 body d-slrs,and Canon 5D and 20D; the D500 is a modern PRO-body type camera...witness the rounded eyepiece...the speed, etc.. The D750 is a "consumer body" with a nice feature set, and a good, full-frame sized sensor in it.
I looked at your photos. I think any modern Nikon camera would be fine for those types of portraiture and wedding shots. D5500,D610,D810, D750,D500, D800, D4,D4s, D3x, any of those cameras could do a great job on those types of shots. BUT--the D500 has become one of the world's best three cameras for action autofocus and SPEED shooting. And, the D500 offers extremely good ISO performance; it has become better than early-generation FX cameras at higher ISO levels.
Look for whatever Black Friday deal you think is the best for you!