For me I usually start tanking bosses with the max EH I have, then drop it to a state where my healers are comfortable, and I don't get any risk to get bursted. I never had any problem with my DPSers holding back because my threat sucked. I won't say that never got called for "make more threat! I can't nuke!!!11!"
Whenever that happened, I usually switched one or two pieces in the next try to test if I could make more threat thanks to my gear without risking my life, and most of the times it was a good decision.
I know that when you are progressing through a new instance people may think you are just being greedy when you want to loot another tank weapon, or certain ring or trinket that could help your aggro/evasion, EH. The best solution is, if the rest of your tank team allows it, to have one tank geared for threat, another for full EH and another for evasion. That way you won't hoard massive amount of loot in one individual and you will have the perfect gear setup for each boss anytime.
In your particular case, your CL's gear can be useful for certain bosses, and yours for another couple. Both of you should talk about who should tank each boss, because if he continue with his threat problems it's gonna be hard for him because all your dpsers will start to blame, or even insulting, his skills about tanking, when we know that it's a matter of gear, not skill.
I hope I explained it correctly, my English is not very good these days xDD