At 3rd level, the dwarf gets a big hit point boost due to another Toughness feat:
Str 16, Dex 14, Con 14, Int 8, Wis 12, Cha 10.
AC 16, HP 41, Hit Dice 3d12 + 2d8
Greataxe: +6 vs. AC, Damage 2d6+1d8+3 or 2d6+3 and Cleave
At 3rd level, the dwarf also gets the Cleave maneuver. For simplicity, I will assume that at the start of the fight, the zombies are standing away from each other, so if the dwarf hits a zombie before he is attacked, he uses his expertise dice to add to damage with Deadly Strike. Once the zombies have attacked the dwarf, he will use his expertise dice to Cleave if he hits and kills a zombie, or to Parry otherwise.
This time round, the dwarf faced three fights of three zombies each. As in the previous fights, luck again favored the zombies, but the dwarf managed to win out in the end.
In the first fight, the dwarf won initiative and killed the first zombie. The two remaining zombies then attacked and both hit him for a total of 10 points of damage. In the next round, however, the dwarf hit and killed the second zombie and used Cleave to attack the last zombie, also killing it.
The dwarf then took a short rest, spending his d8 Hit Dice to regain 6 hit points.
The second fight was pretty much the same as the first, except that only one zombie hit the dwarf, dealing 6 points of damage. The dwarf won initiative and killed one zombie in the first round, then killed the remaining two in the next round with Cleave.
The dwarf then took a second short rest, spending his second d8 Hit Dice and regaining 9 hit points.
In the third fight, the dwarf won initiative but only dealt 8 points of damage, not enough to kill the first zombie. All three zombies attacked the dwarf and two hit, dealing a total of 10 points of damage. However, the dwarf killed two zombies in the next round with Cleave and the remaining zombie in the following round without taking any more damage.
As mentioned, the zombies were again quite lucky, hitting five times out of eight attacks. On the other hand, the dwarf was also quite lucky as he managed to kill two zombies with each of this three Cleave attempts. Apart from the zombie at 1 hp when it was hit, he needed to roll 6+ on 2d6 for the remaining 5.
The dwarf lost a total of 26 hit points over the three fights, which would not have been enough to kill him even if he had not spent any Hit Dice. Again, an "average" difficulty fight with zombies does not seem very difficult.
With 3,800 XP, the dwarf is now 4th level. To make 5th level, he now needs to defeat 21 zombies. I'm going to split this up into four fights of four zombies and one fight of five zombies. Although three zombies is still considered an "average" fight (budget of 555 XP) for a 4th-level character, he's been having a rather easy time so far. The fight with 5 zombies will be close to a "tough" fight (budget of 1115 XP), though.