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This is a good thought, especially that mathematically, the CCG should yield some upsets - certainly more than have actually happened.

I don't think you can avoid the beauty-pageant aspect, though.  If a team is ranked 2nd and loses its CCG, it could very well still get in.  Another team with the same record could be ranked 6th and a loss in their CCG is damning.

Hell, any conference with the #1 team facing another in the top 10 in their CCG should have the top team forfeit in order to guarantee 2 of theirs gets in the playoff.  I know, I know, that's silly, OAM.  Would never happen.  But it's another case of incentivising something ugly. 

something to do away with the conference influencing the officials to make sure the right team wins in the CCG

Possible low rankings in playoff era:
2014
12 lost to 2, 11 lost to 6, 8 lost to 3, and 14 lost to 1.  All of those lower seeds would have had a healthy jump if they pulled the upset.  Keep that in mind for the rankings going forward.
.
2015
10 lost to 1, 14 tied for the XII champ, 20 lost to 7 and 18 lost to 2.  That's pretty scary imo - if #20 or 18 pulled the upset here.  
.
2016
19 lost to 3, 11 and 14 tied for the XII champ, 15 lost to 1.  If 19 VT upsets 3 Clemson here, Clemson stays in it and bumps out a very good team, right?
.
2017
11 played 14 in the PAC.....none of the others were outside the top 10, which is amazing, actually.
.
2018
25 lost to 2, 21 lost to 6, 17 lost to 10.......these are kinda scary.
.
2019
23 lost to 3, 13 beat 5
.
The point of this is that just because we haven't been destroyed by an asteroid impact doesn't mean one isn't headed right for us! 

Possible low rankings in playoff era:
2014
12 lost to 2, 11 lost to 6, 8 lost to 3, and 14 lost to 1.  All of those lower seeds would have had a healthy jump if they pulled the upset.  Keep that in mind for the rankings going forward.
.
2015
10 lost to 1, 14 tied for the XII champ, 20 lost to 7 and 18 lost to 2.  That's pretty scary imo - if #20 or 18 pulled the upset here. 
.
2016
19 lost to 3, 11 and 14 tied for the XII champ, 15 lost to 1.  If 19 VT upsets 3 Clemson here, Clemson stays in it and bumps out a very good team, right?
.
2017
11 played 14 in the PAC.....none of the others were outside the top 10, which is amazing, actually.
.
2018
25 lost to 2, 21 lost to 6, 17 lost to 10.......these are kinda scary.
.
2019
23 lost to 3, 13 beat 5
.
The point of this is that just because we haven't been destroyed by an asteroid impact doesn't mean one isn't headed right for us! 

I just thought of something.

In all those "scary" scenarios you're describing, those teams ranked >10 in a CCG really weren't playing for CFP inclusion. Granted they were playing for the conference championship hardware, and playing for their conference's premier bowl, but a win would NOT have elevated them to CFP (top 4) status. 

With my scenario, every one of those teams will have even more incentive in their CCG to win. I don't know how that will affect upset likelihood [if at all], but my intuitive gut feeling is that it would increase. 

I feel like our fears are in different places.  You want to avoid an unworthy at-large getting in (correct me if I'm wrong) and I'm much more worried about a conference champ being unworthy and getting in.  The at-larges will almost always be top-5 teams, I'm not worried about them.  But there will occasionally be some screwy, BAD conference champs getting in.  That's what bothers me.

No, for me it's not about an unworthy at-large. Truth is that with an 8-team playoff, you could just pick the top 8 ranked teams and you wouldn't have any unworthy teams. The at-large teams in a scenario where bad conference champs are excluded would still be from that group, so I'm not concerned they'll be unworthy. 

What I'm saying is that there WILL be unworthy conference champs getting in from time to time, and IMHO it will be rare enough that it won't bother me. Especially since they'll be HIGHLY unlikely to even make it to the championship game, much less win it all. And if they make it through that gauntlet and win it all? Well, maybe they weren't that unworthy ;-) 

Everyone is terrified that the NY Giants will go from the wild card to Super Bowl champs and take out the team of destiny that's "supposed" to win it. I'm willing to accept that happening every once in a while for making conference championships mean something again. 

That's all agreeable, I think.
With the added incentive to win the CCG by the underdog, is there not a complimentary loss of incentive for a top-3 team to win it?  If they're basically already in?
I know none of this is perfect, but I'm just enjoying the discussion.

Well, we know the psychological nature that has affected both pollsters and quite possibly the committee... It matters when your losses happen. 

Maybe an undefeated SEC team up against another undefeated or 1-loss SEC team in the CCG could lose and still be a shoo-in for one of the at-large bids... But there are only 2 at-large bids.

The question is how far you drop from the loss? Let me put it this way...

If I'm Ohio State and I'm 12-0, ranked #1 heading into the CCG, and I look around and I see an 11-1 Notre Dame behind me and an 11-1 Alabama that is not in its CCG, am I going to feel very good about losing to 10-2 Wisconsin from the opposite division in my CCG? Those two other teams can pass me sitting idle if I lose my CCG. I'm pretty sure I'm not going to feel safe if I lose. 

It's all mental masturbation, yes.

If, say, Nebraska won the B1G and had their choice of Rose or Orange in a playoff setup, would there be that nostalgic feeling to choose the OB over the RB?

I like seeing UGA going back to the Rose Bowl, first since 1942.  (1943?).  Unusual event.