This actually is a very simple question with a simple answer
It's rare any issue is so cut-and-dry, but this one REALLy is.
Without ANY "common sense" or house rules involved, it boils down to this.
Cleave feat SRD text, partial, but the juicy bits:
"The extra attack is with the same weapon and at the same bonus as the attack that dropped the previous creature. You can use this ability once per round."
That's it. If you are charging with true strike active and +99 due to other bonuses, and you total attack is +119,
and IF you kill monster X you get an immediate attack "with the same weapon and at the same bonus as the attack that dropped the previous creature" vs. some monster within reach. That would be +119. Period. Done.
That's crystal clear. True strike bonus applies to cleave, as does height, monster, favored enemy, etc. even if these conditions change (only applied to X not another monster). It's a simple feat, simply written, and does not take into account a LOT of stuff. "Realism" takes a back seat to simplicity of game play in this case. Most people don't really mind.
No recalculation. Just pick another bad guy within reach and cleave. Same "to hit" bonuses.
However, it's also obvious that Frank is (dare I say "as usual") wrong about the damage from cleaving off a charge. Nothing would lead us to assume an extra cleave attack somehow gains the same "type" of attack as the attack that caused the cleave (charging, etc.) which might double/triple damage. The feat says nothing of this, and it's somewhat batty to imply it does. You get an extra attack at a stated "bnous". If you hit, great, do your "normal" damage. If cleave supplied double damage on a charge, it would say so. (along the lines of "if your cleave attack is due to a charge, your cleave attack damage is doubled as the charge was, or tripled in the case of SC...etc.etc. blah blah blah").
To sum: cleave, a simple and clearly-written feat, gives the SAME "to hit" as the attack that "dropped" an enemy, but in no way increases damage dealt.
Now, of course, as is true with a lot of simply-defined rules (such as threatening/flanking), things break down realism-wise rather quickly, causing people to (sensibly) house rule things. But changing the "bonus" to hit on a cleave is a house rule.
Cleave is clear: this is a feat in which "realism" is less important than speed and gameplay.