Sorry, that's not how it works. "Thrash Blade" (any weapon, really) only increases the ATK of the hero by the ATK of the weapon for that combat when you strike with it. "Thrash Blade" only lets you ready your hero after combat conclusion and it has dealt combat damage to the defender for the first time that turn. Then you can propose combat with your hero again in a separate combat and strike again for another +2 ATK for your hero during that combat.
The only time you would get additional ATK from another weapon strike is if it occurred during one combat. For example, if you strike with your "Annihilator" during the defend window, then use "Galway Steamwhistle" to ready your hero and weapon, you can then strike again and increase the ATK of your hero by 3 more for a total of +6 ATK. After the defend window closes, the hero will deal 6 combat damage to the defender.
Hope this helps!
WoW TCG Judge LV2
Player Managment 2
WoW TCG RK2
Disclaimer: All answers provided assume that you have enough resources to exhaust, and are able to pay any other additional costs, in order to play the referenced allies/powers/abilities.