i have messed around with systems for a while and had a big one in my acura. there is no high output alt for the crossfire unless you take it to a shop that rebuilts alts and see if they can rewind it tighter and make it into a high output. my reccomendation do the big three upgrade where you change the wires under the hood for alt to battery, battery to ground and battery to engine i believe double check the last one. Use a capacitor i used a 5 farad which is an overkill more or less 1 farad for every 1000watts i went with 5 since it was not too much. You are right it is a bandaid fix but it will reduce the dimming and help ease up the load. I would recommend an alt but you are SOL. also change your battery to a optima red top not yellow top. Yellow top is not to be used as a starting battery but to be used as a deep cycle battery. Red top is what you put under the hood. lastly get an hid kit it will draw less power 35w instead of 55w and will be brighter it is a no brainer. with hid drawing less power and better output you wont see the dimming.

so to sum it up

do the big three upgrade using all 4agu or 2agu wires
get a cap around 2 farad
change your battery to a red top.
get a hid kit

you might still get some dimming but not as much if any. i did 2 out of the 4 in my acura and it fixed my issues. in the crossfire i plan to do the cap, and the hid kit to start with, then the big three upgrade and last change the battery.