At this point they are probably best off by just retelling SF3 with SF6 and also moving beyond it. I doubt most of the people who played bought SF5 even played SF3 or know the story of it.
If that means more SF3 characters coming back then I'd be okay with it. Remy, Necro, Twelve get slept on too much IMO.
That could be the smartest option in all honesty: retcon parts of the SF3 story but still keep the main story beats and bring in more SF2 characters and most of the new SFV cast (mainly Laura, Zeku, Menat, Falke, Luke, Rashid and maybe G unless he is Q). Spend some time retelling the SF3 story like you said, but remix it and move past it over time.
Could certainly work. How would that work roster-wise though? I'm currently thinking:
SF2: Ryu, Chun-Li, Ken, Zangief, Akuma
SFA: Rose, Sakura, Rolento, Ingrid, Adon
SF3: Remy, Makoto, Dudley, Sean, Necro
SF4: C.Viper, Juri, Abel, Hakan, Decapre
SF5: Luke, Zeku, Menat, G, Fang
...and then another five slots for brand new SF6 characters.
In Street Fighter V we same the idea of having the arcade mode of all main Street Fighter games, and in Rose's endings we saw a hint of needing to travel to the past to avoid certain (post SF3) events to happen.
So probably they'll use that as excuse to rewrite not only SF3, but also the start of the series and who knows if the entire series, or at least to integrate this feature of having arcade modes for all the main SF games in the story of the game and to use it as a bit of reboot or relaunch of the series for the new players.
I'd bet they'll start with 24 characters (+5 secret/hidden/unlockable bosses). And then I think they'll have probably 7 seasons of 5 characters each (new character every two months except once a year where they'd release instead new features, a big rebalance or CPT DLC content). I think they'll make the DLC characters easier to unlock and will focus the monetization more on customization (clothing parts, colors, stages, songs, UI, etc). Since they had a big success with DLC/IAP/season passes, I think they may focus more there and the game may even go F2P if not at launch, some time after it.
Regarding characters I think they'll try to balance between all the series trying to bring back characters who weren't in SFV or USFIV and also the typical fan favorites:
SF1/Pre-SF1: Ryu, Ken, Sagat, Retsu, Lee, Eagle, Geki, Sagat
Final Fight: Cody, Guy, Haggar, Poison, Sodom, Maki, Carlos, Damnd
SFA: Sakura, Karin, Dan, Kage, R. Mika, Nash, Ingrid, Rose
SF2: Chun, Guile, Dhalsim, Zangief, Cammy, Balrog, Vega, M. Bison
SF3: Alex, Yun+Yang, Dudley, Ibuki, Oro, Sean, Makoto, Q
SF4: C.Viper, Juri, Abel, El Fuerte, Hakan, (redesigned) Decapre, Oni, Gouken
SFV: Rashid, Laura, Zeku, G, Menat, Kolin, (redesigned) Ed, (redesigned) Falke
SFVI: Luke, Neo-Shadaloo gorilla, Neo-Shadaloo's ninja/guy with hat, Chun's adopted girl, female Gen's apprentice, Goutetsu, Spanish girl (think Rosalia), native Australian girl
If the game becomes a huge success they could add 3 extra seasons, each one would feature a new character and 4 returning ones.
Regarding game modes I think they'll continue the SFV route but will improve the tutorial and training side to make them more appealing both for newcomers and experienced players, will bring back World Tour and some sort of Rival Schools, Marvel vs Capcom or Dramatic Battle (maybe next gen only, maybe offline only) secondary tag mode.