Suggestion group 1: (modification)
Have bite only indicate a chance of infection, not a guarantee.
Introduce trait to reduce chance.
Allow cleaning wounds with alcohol to prevent infection.
Suggestion group 2: (replacement)
Instead of having bites cause infection, have a “chance of infection” condition.
All injuries contribute a small amount to this, and every some many tics there is a chance of infection based on the odds. (In reality, the odds will be roughly the percent chance of being infected at the end of a given six hour period, and the displayed value will be tenths of a percent of infection)
Zombie bites contribute significantly to this, far more than other injuries. (unless those other injuries are also special sources of infection. This introduces some new and interesting gameplay potential - certain critters could be relatively non-dangerous aside from their high chance of infection.)
Infection chance reduces over time. Using first aid/alcohol/bandages can reduce chance of infection (in order of effectiveness).
No matter the seriousness of the injury, the infection odds should fade over the course of 24 hours to nothing. (this might require simply a vector of infection conditions with timeouts rather than a single infection condition with a variable, but this is a fairly trivial difference)
Character cuts themselves climbing through a window. This gives with a 1% chance of infection after 6 hours (.5% percent after 12, .2% after 18, 0% after 24).
Character is bitten by a zombie. This gives a 50% chance of infection after 6 hours. (25% chance after 12, 12.5% chance after 18, 0% after 24)
Character crawls back and forth through a bunch of rubble, and then gets bitten, all within a couple minutes. 50% plus 20 1% chances mean 70% chance after 6 hours. (35% chance after 12 hours, 16.5% chance after 18 hours, 0% chance after 24)
First Aid use eliminates the highest percent chance in the infection list at the current time.
Alcohol “clean wound” option reduces the time remaining by 50% for the highest percent chance of infection at the current time. (A bite would be reduced 12 hours, meaning the infection chance would only be 25% and you’d only have to worry about half the checks being run, for an even better effectiveness than is immediately obvious)
Bandages work like alcohol, but only reduce the time remaining by 25% instead of 50%.