Starting Hit Points for Weird West Characters

I tend to prefer running RPGs where characters start "at the beginning" and find the tension of vulnerable PCs exploring dangerous environments makes the game a bit more exciting than what you sometimes get when the players know their characters are guaranteed to be able to soak up some punishment in the course of their adventure.

Having said that I've decided that sudden and random character death, even if it's the result of a player missing a clue hinting at danger, isn't all that much fun. Surprise attacks or situations coupled with some sort of dice roll(s) to see if a character is out of the game don't seem like a very good idea. I still like surprises, and I still like that sense of danger - but I think the players either need to be able to take at least one surprise hit, or they need to be able to make meaningful choices about whether to make a risky choice or not.

In classic fantasy RPGs like D&D your starting character has somewhere between 1 and 7 hit points. Sometimes a bit more or less if you have variable hit dice based on class. Weapons and traps do 1-6 damage, or up to 1-10 damage if you use the variable weapon damage rules to go along with the variable hit dice. Either way you're looking at a game where 1st level characters can be killed with a single hit.

What I'd like to avoid is the "more math" solution where all the numbers just get bigger: more hit points, more damage to make things feel exciting again, longer combats, etc.

To create a slightly less lethal game I'm going to use the following changes to hit points in the Weird West campaign:
Starting Hit Points
1st level characters begin the game with 4 hit points for being an exceptional regular human being - an adventurer. This may be modified by one point higher or lower if the character has an exceptional Constitution ability. In addition to this the character gains the maximum for their class hit dice.

For example, a Fighting Man with exceptional Constitution begins the game with 13 hit points (4 + 1 + 8 = 13). A Magician with negatively exceptional Constitution would begin the game with 7 hit points (4 -1 + 4 = 7).

All starting characters will then have between 7 and 13 hit points.

Since weapon damage is limited by a character's class, players may encounter enemies that while attacking with a weapon capable of d8 or d10 damage are only rolling d6 for their attacks against the players. This will be particularly true for lower level encounters when d4 or d6 would more routinely be the maximum an enemy could roll for damage.

Surprise type situations where a character might spring a trap, or fall into a pit will generally do d6 damage as well. "Save or Die" type situations involving either a saving throw or higher amounts of damage will always involve some sort of player decision about acceptable risk rather than be encountered randomly or arbitrarily.

Additionally, the rules for Non-Lethal Combat and Combat Maneuvers means that character defeat does not always mean character death. Players may be more inclined to accept that their PC has been knocked out rather than taking a d4 damage roll against their remaining 2 hit points. These could also be used for traps so that falling in a pit could mean either a sprained ankle (half-movement) OR taking d6 damage.  Some other traps or environmental hazards (like the desert heat) might only do non-lethal damage as well.

I'm optimistic that this is the right balance between improving character longevity at 1st level with keeping the game exciting and not falling into the trap of hit point / damage inflation. I guess we'll find out very soon! :)