[4e HouseRule] Escalation dice to replace expertise

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Hello, after hearing about the escalation dice mechanics I really liked the idea. Quick recap for those that don't know it :
it's is a scaling bonus that is applied for attack rolls during combat. It start at 0 on the first round and then increase by 1 every round (the current value of the bonus is materialize by a face up d6 dice visible to everyone, hence the name of the mechanics).
There are then several variation, like give the bonus to attack rolls only, or attack rolls and damage rolls. Give the bonus to PC only, PC, elite and solos only, or everyone.
Then on top of it you can build some additional mechanics that depends on it, like a power that is usable only if the esclation dice is 2+ (ie not usable before third round), some power that can increase the value of the escalation dice, etc...

On the other side of the equation, I've always found the expertise feat to be rather boring (at least the static bonus part)

So here is the idea : remove the static bonus part of the expertise feat (but keep the additional benefit like increase forced movement by one for orb expertise for instance), and to compensate give an escalation dice bonus to all PC. The bonus would be dice value * 1/3 for heroic tier, dice value * 2/3 for paragon, and dice value for epic which gives us the following bonus :

______Bonus____Heroic_____Paragon_____Epic
Round
1............................0....................0...................0
2............................0....................1...................1
3............................1....................1...................2
4............................1....................2...................3
5............................1....................3...................4
6............................2....................3...................5
7+ .........................2....................4...................6

This gives us an everage bonus (on 7 rounds) of 1 at heroic, 2 at paragon, and 3 at epic

The expected benefit of this house rule would be :
- Bring back choice in feat choice by removing the expertise feat 'tax'
- Discourage going full nova at the begining of the encounter : either use it early for nova, or wait a bit more to have a better chance of landing

Possible downside : Even though the average is equal to the expertise bonus, it might be a bit less powerfull as you don't get a bonus equivalent to expertise bonus before 4th round .... This would maybe slow down the fights, which is opposite to the goal of the escalation dice....

Possible alternative would be to use this slightlty modifed table (using rounded up value instead of just rounded)
______Bonus____Heroic_____Paragon_____Epic
Round
1............................0....................0...................0
2............................1....................1...................1
3............................1....................2...................2
4............................1....................2...................3
5............................2....................3...................4
6............................2....................4...................5
7+ .........................2....................4...................6 

or starting the bonus directly on the first round (or both : starting directly on the first round and using second table values)

Other possible downside, is the use of fractions, which are not easily repesented by a dice. Possible solution for this would be to just use different dice per tier :
______Bonus____Heroic(d4)_Paragon(d6)_Epic(d8)
Round
1............................0....................0...................0
2............................1....................1...................1
3............................2....................2...................2
4............................3....................3...................3
5............................4....................4...................4
6............................4....................5...................5
7............................4....................6...................6
8............................4....................6...................7
9............................4....................6...................8 

This would be easier to track, and would also probably speed up the fight a bit


So what do you think ? Which version (if any) would be better ?

TLDR : Remove the bonus giving by expertise feat and replace it by escalation dice bonus, good idea ?
Your alternative ideas are neat, good thinking. I like the first idea (fractions to the dice roll escalation), since it's straightfoward for my play style.
The expected benefit of this house rule would be :

- Bring back choice in feat choice by removing the expertise feat 'tax'
- Discourage going full nova at the begining of the encounter : either use it early for nova, or wait a bit more to have a better chance of landing

I also have a house rule in my game based on the 13th age escalation mechanic. The rule is:

If you use an action point while you or an ally is bloodied, you may add an escalating bonus equal to the combat round to atks & dmg for that action (i.e., during round 4 you would get an untyped +4/+4 bonus).

This rule does not discourage anything, but it does provide additional options if PCs choose not to go full nova at the beginning of the encounter - if they want a multi-target daily power to be extra-amazing they have some incentive to wait until Round 3 or 4. But the main advantage of this houserule is for the GM - it provides solo monsters and elites with more interesting tactical choices, and makes big baddies much more dangerous after they get bloodied, which can help to reduce the feeling of combat grind.