As you guessed, this little trick doesn't work. There are only two ways to activate an ability or cast a spell while another spell or ability is resolving, and your combo doesn't fall into either one:
- If the spell/ability that's resolving lets a player pay mana, that player can activate mana abilities.
- If the spell/ability currently resolving explicitly tells you to cast a spell or allows you to cast a spell, you can cast that spell. Even in this case, the newly cast spell waits on the stack until the current spell/ability finishes resolving.
CR 608.2f If an effect gives a player the option to pay mana, he or she may activate mana abilities before taking that action. If an effect specifically instructs or allows a player to cast a spell during resolution, he or she does so by putting that spell on top of the stack, then continuing to cast it by following the steps in rules 601.2a–h, except no player receives priority after it's cast. The currently resolving spell or ability then continues to resolve, which may include casting other spells this way. No other spells can normally be cast and no other abilities can normally be activated during resolution.