Btukfyl

Can I trigger an instant speed “Act of Treason” type effect (like with a Vedalken Orrery or Jeering Instigator, for example) to grab a Seedborn Muse before an opponent’s untap and untap all my permanents?

Well, obviously there will be points in the game prior to your opponent's untap step. For instance, on the turn before your opponents turn, you can grab the Seedborn Muse during the ending phase. If that's your turn, you can announce after your second main phase "I am casting Act of Treason using Vedalken Orrery's ability". Or, if you're in a multiplayer game, if that's another player's turn, then when that other player announces the end of their turn, you can say the same; when a player says they're ending their turn, they're just passing priority, and other players have the chance to take actions before the turn actually ends.

However, there are two problems.

First, Act of Treason only lasts until end of turn. If you do this during the end step you will pass Seedborn Muse back more or less immediately after it. You will not have Seedborn Muse by the time the next turn starts and it will be back under the control of whoever had it last.

Second, once the untap phase begins, it's too late to do anything to affect what happens in the untap phase. Even when something is "instant", you still have to wait until you receive priority, and

No player receives priority during this step so spells or abilities cannot be played. — Rules for the Beginning Phase

You first receive priority during your Upkeep, by which time Seedborn Muse has already had its effect and it is too late for gaining control of it to do much for you.

There are ways to take control of a Seedborn Muse and use its ability to untap your permanents, but an effect that only lasts until end of turn like on Act of Treason won't help you there.

Seedborn Muse's ability happens during the untap step, the very first thing in a turn. You have no opportunity to act in that same turn before that happens. And if you use an effect like on Act of Treason or Jeering Instigator to take control of the Seedborn Muse on a previous turn, that effect giving you control of it will end during that same turn, so it will be back under its owner's control by the time you get to the next untap step. You would need a longer-term control effect like Control Magic to actually be able to use the Seedborn Muse's ability.