803D4 - what integrated we thinking is a better match? Hegel? McIntosh? Other?

Depends completely on what specific improvements you’re looking for and what sound characteristics are most important to you. 

I've owned and heard at several audio shows B&W speakers paired with Musical Fidelity integrateds - good combo.

Have you considered the Primaluna EVO 300 Floyd integrated amp. I’m using is with an earlier B&W 803 diamond speaker and it’s great. It has plenty of grunt that the speaker needs and a tube preamp section. It’s really a fantastic amp. 
 

Good luck in your search. 

I was under the olde school belief that separates are always better... that tide has turned. Several great one box solutions out now. For my desktop I have a Hegel 190, in my main the McIntosh MA 12000. They both do what they are designed to do - and exceptionally well. Even on the digital path - the Wadax Studio player (one box) has great reviews....out of my price point; but when you consider separates: power cords, interconnects, a DAC, CD/SACD player, and streamer in one package...the Wadax price is more approachable.

With the McIntosh MA series – you will have more paths/interconnects than you will ever need/use & the tube front end with the SS back – is exceptional. Many have mentioned good synergy with McIntosh with B&W speakers…I would always want a first-hand  demo or listening session first for this type of purchase…

MA9500

Pass Int250 I ran a pair of N803s with pass X250.5 and it was a great combo. This integrated should do just fine

Boulder 866

I love B&W sound. It’s a polarizing brand but the 800 series are awesome speakers. There will be those who prefer other speakers and those who never owned a pair of B&Ws but love to hate the brand.