I have been working with these amps for a while now and have tried so many different things.
Each modification is usually to taste, there isn't too many things you can do to make the amp sound better, but the ones that work make a HUGE difference. You can get a little complex but in the end if you have the right parts a lot of mods isn't necessary. The biggest issue is the speaker. The cab size is small so trying to shoe horn a 10 in there doesn't help much. Using a slightly higher power 8 is much better and ditching the cab by putting it into to storage is a better choice. Either make a head or a combo with 2 8" speakers or 1 10" speaker. SE amps usually have a certain harshness on the highs that certain speakers bring out and it's a disastrous combination. One speaker comes to mind and that's the worst I ever heard with a champ, a Jensen reissue C10Q. One of the best is the Eminence Copperhead for Jensen type tones and the Celestion 10" greenback for more of that Brit sound. I have tried more speakers with these amps then I care to remember, everything from older Jensens 8"/10"/12" of all models to Celestion Golds, greens, blues, eminence 10s of every model, D208 JBLs......almost everything out there.
If someone were to hand me a stock 70's Champ and say make it sound right, like one of it's bigger brothers from the 1960's era BF family but with a little more umph. I would simply do the following which includes using BF specs: Take out the NFB, Put in a larger OT with a 4/8 ohm tap, add more filtering with another leg on your B+ rail and a BFDR choke(if you are staying with a 6V6 use the 1K 5 watt resistor and a 470 5 watt on the screen), You might also add a 10 watt 100 or more ohm resistor coming from the rec tube to cut down some voltage, add a 1.5K resistor on the 6V6 grid, use the 1.5K/25mfd combination on the preamp's second cathode, take out the second and useless input and replace it with a 25KL mid control(use both 68K resistors in parallel or a 33K and remove the 15K resistor on the bass pot), and wire up the heaters with twisted pairs and 2/100 ohm resistors to ground to help with noise. The extra gain will add noise. Replace ALL electrolytics, replace all drifted resistors especially the 100K in the tonestack, and even replace the ceramic disc 250pf with a silver mica. Since you are already there I would also try either the Jupiter caps or the SOZO blue caps, I bet they sound a bit better then the originals.