I don't have a problem with a more struggle-like game style. Still if looking at the problem realistically, Stake won't be able to do anything with the hospital system in his current condition. Just for the math: with LOG 7 and Hacking 6, i roll 15 dice if i'm on the same grid as the host i'm hacking and not in hidden mode, to get access; against this, the hospital uses its Device Rating 7 and Firewall 10, for 17 dice. Even on my best day, with full Edge pool (currently empty), it is a stretch to spend time in there. When wounded (-2 to all checks), near impossible. I'd still try it if Stake weren't wounded, because i'd have a chance, it might just be i'd have to bail very quickly.
I also don't know if it is possible, but we should try to get some "help" to access. Nicking an employee of his commlink which might have access data, examining the tag and trying to extract credentials, all could possibly help (there's no game mechanics for that, i figured Inca would tell me if i'm going at it the wrong way). I think all of these would take time. And don't forget that we still have a protected file, which i can try to crack again after some rest.
@Inca: i changed my mind, instead of the skill groups, i'd like to improve my hacking skill to 7.