With fewer Attack Action disparity between players (some get one, some get two), altering the order of Narrations is not THAT detrimental to game flow. It essentially puts faster characters on the GM's left and circles clockwise to the slower players on the GM's right. (Think about just sitting people where they would normally land in the Narrative Order).
The player that wants to go faster can always just spend a Plot Point and go first.
I agree that "Game Level" is not a good way to determine Initiative. NPCs do not have a stated level and there is no method of "graduating" from Street to Prime, etc.
The main downside to your proposed initiative calculation is that it does not take the Matrix or Matrix icons into consideration. Previously fast VR-capable characters are going to go last based on having an AGI dump-stat. Think about using AGI or LOG (whichever is higher) so that VR or IC (who have no AGI stat) can still get a fair shake at going first.
The other downside is that, if you are rolling dice pools and counting hits, you are going to effectively round down their dice pool to 1/3rd. This causes a lot of duplicate hit scores. My experience is that you end up having all the players at the table with 3-4 hits and the enemy NPCs with 3-4 hits and lots of ties that you have to break anyways.
I have another method that I use: Roll 2d6 and add them together. Add the higher of your AGI or LOG. Then players who want to spend Plot Points may add 1d6 for each PP spent. Players with free PP can reliably get higher scores by spending them but they do not have to. That sets the order for the whole combat Then if a player wants to Seize the Initiative, they can narrate first for that Turn only. Players with Combat Paralysis go last for that Turn only.