Though I cannot phantom for the life of me why on earth an anime viewer would walk into a fanfic thread, and I do think all fanfic entries need to be hidden under a Spoiler Tag if it happens after the First floor is cleared, this is quite an awkward situation.
In the Furinkanzen scenario, the odds are high that much of the Beater nonsense may well be averted. After all, why hold all 1000 Beta Players responsible, when some of the Top Clearer Guilds made it this far thanks to Beta Players guiding the way? This is a very interesting scenario in my opinion, but I suspect once the Executions start, word would get out that the Guilds on the Frontline need Beta Players, if there are rather open cases of guilds with Beta Players helping.
Indeed, if Kirito's example does trigger a wave of aggressive front-line guild recruitment of Beta Players, odds are, most big guilds at the front-lines have no problems with the Beta Player issue. It may well be the Middle Guilds that aren't as happy with the situation, at least at first. If the "executions" still takes place, odds are, many Beta Players would cave fast and join a Guild for safety, and to claim that they are indeed doing their part, if indeed Kirito's joining triggers aggressive recruitment of Guild Players.
Of course, there could also be "Guild" Envy- one potential problem is that Furinkanzen get's branded a Beater Guild, for having exclusive assess to a single Beta Player.
The biggest butterfly would be the lack of "First Day", I think. Then again, Kirito's first breakdown might occur later, after the Anneal Blades, or after seeing some players die.
Another point to note: it is likely that Furinkanzen would find themselves on the front, roughly the same time Asuna goes on her Suicidal Rampage at the start of Aria. Odds are, many other groups ran into Asuna, so I think it is a justifiable plot coincidence for Asuna to run into Kirito still, plus or minus a few days. The events in Aria concerning Asuna might transpire in much the same way, though the +4 Anneal Blade Incident would acquire the dimensions of a Guild Rivalry of sorts, I'd presume.
The second possibility is that two or so weeks in, once Kirito is satisfied that Furinkanzen can stand on it's own, Kirito would leave to solo, or to accept other tutoring requests from other Guilds. That however, would either lead to a spiraling cast of OCs, Kirito dying at the First Boss, or even an earlier meeting with Sachi- the last is very interesting, but unlikely, and Sachi is not Asuna, so there's a good chance that he'd still get Sachi killed.
It is also possible that the Black Cats do get absorbed into Klein's guild. Indeed, Klein's guild may have a surprisingly large number of girls in them, if we want to go through the coincidence route. By April 2023, in the best route, we'd get Asuna and Sachi in Furinkanzen. If Sachi dies this time, it may well be a big hammer blow to both Asuna and Kirito - for Asuna it might be about as painful as seeing Yuuki die, for instance. It might even lead to an earlier Kirito x Asuna. If not, then a potentially awkward triangle might result, with Kirito leaning Asuna and Sachi... well Imouto zoned.
Now, if we take that Sachi is doomed to die, then odds are, she'd die in a different way. It will hit Kirito hard, but with a guild support structure and if Asuna was with Kirito at this point, not as hard as RNR.
It IS possible to get Sachi, Asuna and Silica and even Lizbeth in the same guild together, though without Asuna in the KoB, the butterflies would be huge. On the other hand, Klein's guild might be quite considerable - two principal sections - the Clearer Frontline Sections, and Middle Guild portion of Mid-ranking players, who acts as eyes and ears, assist to amass sufficient guild funds for resupply, engage in back-line skilling support. If there is a Middle guild, and Kirito frequently makes trips back to the Mid-levels, odds are, he's going to run into Silica, since Silica did make a good name for herself as a Mid-ranking player.
For all we know, at the point of RNR, Lizbeth may already be Furinkanzen's offical blacksmith, Silica the closest they have to an emergency healer, etc...
The big question is whether Heartcliff's identity can be unmasked. Indeed, I've wondered how Heartcliff convinced Asuna to join the KoB. Heartcliff may still be able to poach Asuna away- I'm sure personnel exchanges between Guilds was not necessarily unheard of.
By this point, even if we got the main cast remains intact (and no doubt, plenty of OCs will be in this story), we might get a happier Kirito and a story so far, far off the rails that everything would be different. Chances are still good though that Kirito may be able to unmask Heartcliff before level 100 and likely another 1000 players dead- the only question is when.
Whatever the case, we'd be feeling the knock-on effects far down the road. Chances are very high that Kirito's Unrequited Love Alliance would be even larger this time.