The Friedman is definitely the darkest and muddiest profile in this set. It's one that I have a hard time using but it can sound good with the right guitar at the right settings I guess. If a different cab makes it work better, that's what I would recommend.
As far as sounding like the video, I think much of it has to do with the guitar and with your speakers. I have a really hard time getting my Kemper to sound "right" through my studio monitors at home. I only trust my Ultimate Ears UE7s or my Xitone cab when I'm tweaking because all headphones and speakers have a pretty drastic eq curve even though they are supposedly "flat". It's what you have and get used to and tweak to that can make it work for you. Maybe my UE7s aren't flat but they're just what I'm used to so they sound "right".
I tried these profiles with my Strat through my monitors and they sounded ok, but as soon as I picked up my Anderson tele they all sounded better, so different pickups are part of the equation as well. The good news, I guess, is that there are lots of free tonal options available so hopefully you can find profiles that work for you. Even after making hundreds of profiles, I still gravitate toward the same 10-15.
Following on from what Michael said here and also from a previous thread, I stopped using my headphones and instead have been using good quality in-ear earphones by etymotic. Makes a large difference to the clarity of the tones as good in-ears don't have as much bass as headphones, even neutral ones made for mixing such as my sennheiser hd600s. If you have some decent earphones I'd suggest practising through those instead.
Michael, your comment about using UE7s makes sense to me as now that I'm using in-ears the tones sound a lot more balanced! Cheers!
Eltzejupp, now that I've re-read your post it would appear you've tried different setups already. However I'd still recommend trying some in-ears. Also, might be an obvious one but how old are your guitar strings? Have you tried going through the spdif to your interface ? I have found that using spdif yields better tones, with more top end. Also is there a difference in tone between the headphone output straight from the Kemper, and the tone you have recorded via your audio interface? If there is difference and you have been using analog outputs from the Kemper then this may give you clue that you're losing some top end. Might be a good idea to compare recorded clips using the analog outputs and spdif outputs if you're able.