Streamlined Saving Throws and Skill Checks

In addition to attack and weapon rolls the next most common dice rolls in the game are Saving Throws and Skill Checks (if you include a Rogue / Specialist / Thief style character).

They're a bit all over the place with different dice, tables, roll high, roll low, and either vary wildly in % success between high and low level or use lots of math to keep things relatively balanced in probability.

So here's what I'm thinking of doing to streamline things:
All checks are based on a d6 roll with 5+ being a success
That applies to everything: surviving the rattlesnake bite, jumping over that crevice, sneaking up on those weird cattle rustlers, even repairing that robot head you carry around in your carpet bag.
This die roll is modified by the following:
+/- Higher or Lower level challenge
+/- Relevant ability modifier
+ Class Bonus
Some examples:

A Cowboy bitten by a rattlesnake needs to make a check against the poison. He needs to roll a 5 or more with the following modifiers: +1 for being 2nd level (the Rattlesnake is a 0 Level challenge), +1 for being Rugged (Ability modifier), +1 for Class (checks against Death) -- which is +3 in total. A roll of 2 or more is a success.

A Kid is climbing out the window of an old mansion to escape an Animated Terracotta Warrior. He needs to make a check to see if he loses any stamina tumbling to the ground. He needs to roll a 5 or more with the following modifiers: +1 for being 3rd level (the DM set this as a level 1 challenge), +1 for being Slippery (Ability Modifier) -- which is +2 in total. A roll of 3 or more is a success.

A Scholar is trying to activate the alien artifact they discovered in the old silver mine. He needs to roll a 5 or more with the following modifiers: -1 for being 4th level (the DM set this as a level 6 challenge), +1 for being well-read (Ability Modifier) -- which is +0 in total. A roll of 5 or more is a success.

If the challenge is more than 2 levels higher or lower in level the DM may choose to increase the bonus or penalty to the roll. This could result in some checks that automatically succeed (1+) and some that are impossible (7+) for some characters, which seems quite reasonable.