There are several variables to consider before I could give a hard statement concerning extended tenure.
1. Is there visible improvements in team play.
2. Recruiting. Are the new recruits making an impact on the team. Rankings non withstanding.
3. Staff. Is there cohesiveness and consistency.
4. Portal. The outlet is available, so is Beamer taking advantage.
5. Attrition. Is Beamer able to keep the players and or staff with the program.
As of now today, no I would not be in favor of 3 more years. Could that change by end of next year, yes of course, but that would mean an improvement in all the of the mentioned above.
Here is how I see it based on your criteria, which I 100% agree with btw:
1. Improvement - Nobody likes our record. However, the UGA and UF games last year were unmitigated disasters. Did we improve on how we competed with those two teams year over year? Yes. Ga St game vs UNC game - Do we beat Ga St without the blocked punts? We had 7 drives that ended in punts or INTs. It wasn't pretty. I'm not sure we played any worse against UNC than we did GA St. Results against Mizzu were the same. UT flipped. Beat a bad MSU team, lost to a bad Ark team last year. All in all, even though the record doesn't show, has the level of play relative to how we've played opponents improved? I'd say yes, marginally. We'll see if it holds.
2. Recruiting - The 22 class produced Nick E and DQ. Both freshman all Americans that are struggling a little with different positions, that had 2 NFL CBs removed from the secondary. There are a bunch of 23 guys that are playing. Hard to measure too much b/c they're true freshmen, and on defense, it's hard to gauge due to coaching deficiencies. People disagree, and that's fine, but Harbor is progressing and becoming a weapon. 4 catches with a 25.5 yd average, 1 TD. He's going to be a stud. We would probably have 3 true freshman OL starting if Anderson didn't get hurt. There is no doubt his guys are making an impact.
3. Staff - this is a mark against him, really no way to sugar coat it. I like the Logg hire. And I think when he gets ahold of Sellers and has a QB that he can also use in the running game it's going to be really exciting to watch. That's what he really wants to do. If he can make a move on DC and have similar results, all is well.
4. Portal - The portal woes this year were exaggerated. The portal is not the reason for our record this year. He replaced Bells production. We could have used Lloyd though. Burch wasn't a big loss. The biggest issue we have is that we lost two really good CBs to the draft and had nothing behind them, not the portal. But overall, I'm pleased. He's not going to bat 1.000. Getting Ratt, Juice, Adkins, Mario, Nick G have all been big wins.
5. Attrition - We will get a better measure as his guys get in there. Say what you will, but he and Muschamp go about things differently. Muschamp pitched a NFL training camp to these guys. Beamer isn't doing that, so you got two different kind of players there.
Lets see how this year plays out. I need to see 4 years before I say yes to 6. If we flame out and go 4-8 this year, and 3-9 next, he's in trouble. But I'm still a believer that he'll get it right.