BRC's (Hopefully) Simplified grapple rules

[BRC]

This is me attempting to simplify grapple checks. I think I succeeded, but I'm not sure. My real hope is to cut down on the random rolling, especially that associated with engaging a grapple.
BRC’s simplified grapple rules.
When an opponent attempts to grapple you, you have three options.
1: Dodge. Your opponent makes a melee touch attack against you, if they hit you are automatically grappled and are assumed to have lost the first grapple round. If the grapple succeeds they have the advantage.
2: Attack. You may choose to make an Attack of opportunity against the grappler. If this misses you are Grappled. If it hits and was made using a reach weapon, the grapple attempt fails. If it hits and deals more than twice their fort save the grapple fails, if the Grappler is immune to nonlethal damage the grapple succeeds anyway (Unless it kills them). If the grapple succeeds they have the advantage.
3: Counter grapple. You make an opposed grapple check with your opponent. Whoever wins has the advantage.
ADVANTAGE:
At the beginning of either grappler’s turn, an opposed grapple check is rolled to determine who has advantage. If you hold the advantage at the beginning of this round, you get a +2 bonus on this roll.
Once you have won the advantage, you may:
1) Disengage the Grapple
2) Attack with an unarmed strike, natural weapon, or light weapon.
3) Grab an object or weapon from your opponent (with an opposed grapple check)
4) Pin your opponent (With an opposed grapple check)
5) Trip your opponent (with an opposed grapple check)
6) Push your opponent (opposed grapple check). If you win they move back 5 feet, the grapple is disengaged, and the loser must make a balance check (DC equal to your roll) or fall prone.
7) Cast a spell. Make a concentration check (DC 20). If the spell has somatic components, you automatically give up the advantage.
If you don’t have the advantage, you may make an escape artist check vs opponents grapple check to disengage the grapple.
The Improved Grapple feat adds a +2 bonus on all grapple checks.

[Temotei]

Does the +2 bonus you attribute to Improved Grapple stack with the current +4 bonus from the feat?

[BRC]

Does the +2 bonus you attribute to Improved Grapple stack with the current +4 bonus from the feat?

I dunno, let me think about it. To be honest, I forgot about the +4 bonus, I put the +2 in there because the "Dosn't provoke AoO" isn't as relevant with this ruleset. But the +4 bonus itself may be enough for the feat to work.