Full disclosure: I have absolutely no experience with Savage Worlds. That said, I do have some experience devising game mechanics that work, both here and across a real table.
Mahatatain:
To speed it up you might want PCs to declare their actions without knowing the initiative order (so that players can post when they're able to rather than in initiative order) and then draw cards for initiative yourself to decide the order in which you resolve PC actions.
It's also possible for each player to draw their own initiative card, post as they can, and then let the GM sort out the action in a single reply post.
Is there a requirement in Savage Worlds during initiative that all players draw from the same deck? If so, yeah, the GM drawing for all players would be the way to go. In that case, I'd suggest that some method of establishing a drawing order would need to be discussed and that drawing order published as part of the game rules.
In case it is useful, the dice roller link might look something like:
[dice=5d54 system=deck54 target=5 record=yes text="Five draws from a deck of 54" memo="Five draws from a deck of 54"]
This message was last edited by the user at 21:02, Fri 07 Dec 2018.