The problem
It is my understanding that charm pets were too powerful with their previous implementation because they could easily be stunned when they broke, completely trivializing the danger of a charm-break and therefore the party effectively got an insanely powerful pet with no real cost or threat. However, I feel that the current state of charm pets makes them generally not worth using. I know you are currently exploring solutions and I wanted to share my two cents, if they're worth that.

Overall, I would rather the risk of charming to be increased so that the damage of charm pets can be, at least partially, restored. I think that the risk of charm breaks should be tuned alongside damage when looking for the solution.

My proposal
To that end, I recommend creating a status effect for a charmed mob and the caster. While this status effect exists, any cc applied to the charmed creature is also applied to the player that cast the charm. So if you stun the charm-broken mob, you also stun the player responsible for re-charming them. Rooting would be preferable to stuns in this situation, but there would also be the risk of rooting the charm-broken mob too close to the charmer, likely getting them killed. Positioning becomes more important. Teamwork and communication become more important to prevent a wipe.

I believe that this preserves the high octane play-style of pet charming while creating a high enough risk factor that it does not become the default optimal choice for every encounter. It also thematically makes sense that a player charming a creature could suffer debuffs that the creature suffers.

I don't intend this to be an additional punishment on top of the current damage reduction. My proposal is to restore much of the damage and utility that made charm so powerful in the first place, potentially including its ability to serve as a tank, while making the consequences of a charm break substantially more dangerous. I think that level of power can be justified, but only if using it introduces a meaningful risk of catastrophic failure that can't be trivially bypassed.

Rather than balancing charm primarily around how much damage the pet deals, I'd like to see it balanced around the relationship between its power and the risk of controlling it. A charmer who manages that risk successfully should be exceptionally effective. A charmer who misjudges it should be capable of putting the entire group in serious danger.

Possible variations (just ideas, feel free to pick and choose)
1) It could either be applied when the charm breaks, or when the charm breaks and while the mob is charmed. If it is also applied while the mob is charmed, then giving mobs the ability to cc will punish the use of charm pets, allowing encounters to be designed to promote alternative play-styles.

2) The status effect could be made dispel-able, but dispelling the buff should only dispel the status effect and not any additional debuffs. This way dispelling is a valid solution, but it has to be cast twice to work, or cast before the cc is used.

This gives a few interesting variables to further tune and balance charming as a game mechanic:
Duration of the status effect.
Duration of cc modifier (so cc could last longer or shorter on the charmer than it does on the broken charm.)
CC cast on the broken-charm could burn the charmer (either health or mana).
CC/damage could give resistance to future charm effects.

Concerns
1) Players can grief each other by purposefully casting cc on charm breaks. I recommend a clear visual indicator when a mob has this status effect. I could see this falling under the umbrella of the anti-griefing rules instead of adapting the mechanics to prevent it. So much of this game already relies on social expectations that I don't think it is a hand wave to suggest as a real solution. If there absolutely had to be a solution for this, then it may make sense to give the charmer a button, in the form of an ability or clicking off their status effect, that locks them out of the opportunity to re-charm the mob, but also prevents them from getting the shared cc.

2) Players can get aggro on the broken charm, then stun/mez the broken charm and charmer, run to the zoneline, then the broken charm will run away from the charmer when the cc ends, and the charmer just casts gate, giving everyone an easy way to escape. I think this interaction should be designed so that it doesn't become a reliable, consequence-free escape strategy. A charm break should be capable of forcing the group to choose between attempting a dangerous recovery and abandoning the charmer to save the rest of the party. I envision the re-charm failing twice, the tank is already low on health, the healer is oom, and a last desperate mez is put on the charm break, also locking down the charmer. The rest of the party barely kills the mob they were fighting, but now there is a broken charm sitting in camp with a timer. The charmer makes the call and tells the rest of the party to run, knowing that when that timer runs out, they'll die.

Conclusion
I think charm pets are a really cool mechanic. I have fond memories of using charm pets in EQ to tank when we didn't have a tank, to provide a dramatic DPS increase, and getting wiped because my charm broke and then was resisted twice and now I didn't have the mana for any cc and now we are fighting two difficult mobs instead of one. I loved that I was very rarely "expected" to use charms because everyone understood the risk, but when it worked everyone appreciated it. My other abilities were strong enough, and I never had the mana to reliably use my other abilities and focus on a charm, and I think these were the factors that ensured people were okay with my decision to not charm, and often asked me not to so they could more reliably get their buffs.

It was always impressive to see a caster use charm pets well and when they did, it stuck out and often earned them a friend invite.