ok this will add to the other two solutions and together you definitely can't go wrong... :P
fire axe is a good idea, get the ammo from sporting goods and chainsaw was useful, but i found that i had grenades and molotovs i never would use, so i suggest just discarding when you get those to make room for something better. the reason is that since the zombies pretty much come after you the whole time you won't find yourself in a full building too often. of course if you are in that situation then go for it. also marbles weren't worth my travel time. though alternate food saved me one time. which brings me to the next important point:
do not ever end your turn standing right next to a zombie if you can help it. when you start the turn you have to fight before you roll and if you can get stuck in a situation where you have no choice but to lose. using the second solution and going back to the menu, while sort of cheap, was very helpful. for example if you do start next to a zombie and you roll 2, reroll two, reroll 1. then you have no choice but to spend 3 bullets. as long as you don't press spend you can go back and just spend 2 the first roll and save your hearts. it saves after any pre-roll fight and after the last fight when you run out of movement spaces. however, if you are fast on your last fight you can reset your roll. just watch the die and be ready to press the button as soon as you see the bad roll.
you might also start to notice some patterns. as mentioned it is not totally random. here's the technique that got me through this. i would roll and my first zombie i'd get a 6, then next a 5, but always a 2 after that. so i would just end my turn one space away from third zombie instead of fighting it. next turn would be a 2 so i wouldn't fight it, just make sure to end one space away again. next turn i think was a 1. so you keep going until you get a turn that starts you with a high roll. when you get the high roll see how many guys you can kill before you stop, then go back to the retreat mode. anyway this is getting long so i think that's plenty.