According to Boardgame Geek stats the best board games have a lowerl random factor, this is not the case with Tannhauser. For example a bad first shock roll that gets a key character killed on the early game might end most chances to win a game, likewise in other "sensitive rolls". Basically the feeling I have is that the "Lucky silver bullet" that comes out of nowhere destroying your carefully laid strategy should be at least minimized.
There are several options to limit the random factor without altering too much the rules, the first that comes to my mind are rerolls, a very nice feature of BloodBowl: Each faction gets a number of rerolls they might use during an entire game (not a turn), thus preventing catastrophic rolls that can wreck a game and providing a bonus to a sound strategy.
So, how many rerolls do a team get? my first proposal would be as many as command points so 2-3 per game. Then I would add 1 bonus reroll per game to the team with highest initial initiative modifier (if both teams are tied no bonus reroll), this way we favor a bit more the hero's command packs that have an initiative modifier.
Another way to limit the random factor is changing the rules on duels, normally in case of ties the "defender" wins the duel. I would change it so the character with higest base value wins tied rolls, in case both characters have the same base value then the defender wins the ties. This affect mainly bull rushes, it is a bonus for these strategies in which a path is blocked on purpose and for choosing the right guy for the right task.
The same counters we use for the cps might be use to mark rerolls, using the ones belonging to the factions you are not playing with would help to avoid confusion as they have different backgrounc color.
Anyone willing to playtest this?