Something that came across my mind earlier today. How about making the first two turns get a little more done?
Instead of setting up the board as normal each player receives two hands of 4 Apprentice and 1 Militia. Then in reverse turn order (however you decide it) each player can buy from the deck as they choose.
Example...player number 4 goes into the deck and pulls out two Void Initiate and one Temple Librarian. Then around the table to player one.
Then you repeat this one more time beginning with player 4 again.
Once all players have done this twice shuffle up the player decks, the center deck, and place the available cards out to begin the game as normal with player number 1.
I think this might help with some of the "lack of strategy" talk going on.
The other option is to limit each purchase to a specific "faction" for each purchase round while setting up.
One other variant that I have not thought fully through is have each player choose a "faction" and hand them all of that factions cards from the center deck. Then go after the monsters to see who will win. Mechana might be busted by doing this. You would most likely need to just count honor tokens and not the value on the cards to balance this one out?
Enjoy at your leisure.
I appreciate these ideas, because I've heard "lack of strategy" talk too (especially from Dominion fans). Personally, I like the element of chance (and find Dominion too mechanical), and think there's still bags of strategy taking advantage of what comes up whilst not giving it away.
However, I'm not keen on stuffing your deck. Maybe there's a way to drafting, like the Race for the Galaxy variant, which I enjoy (players build their own draw pile in a set up phase - 5 cards are dealt to each player, you pick 1 and pass the rest on, rinse and repeat).
What I've tried for more interesting early turns is just starting with just 2 militia and 3 apprentices. This turbo-charges deck turnover and avoids that annoying initial 4-1 split. It does reduce the value of the Void strategy though, and can magnify the advantage of a lucky early hero buy (perhaps this could be combined with the 4x3 or 2x6 variants to avoid that).
Another idea to promote a faction strategy would be to divide the cards by type. Shuffle the 5 stacks and split the monsters so there's a deck for each centre row slot. I wanted to play this way to avoid the droughts that can stymie power building or Mechana strategies, but I feel it can make play too like the Dominion race to exhaust VP.