Ok, for the record -- and to brag -- here is, what I did. From this (the quad-contraption had one of the valves busted, rendering the rest useless):
to this shiny and new -- though not yet fastened to the wall:
The water source is still the same sillcock
The black pipe (hose?) on the right is buried one, it goes all the way to the backyard's garden (purchased the house with it). Whereas before it was connecting to the manifold using the garden threads, now it has its own push-connection.
The white pipe on the left goes up to the deck -- to feed the children's sprinklers. It also used to connect to the manifold.
Instead of the two free openings I used to have, I now have three -- and one of them has regular NP-threads instead of the "garden" ones. (I'm thinking of switching everything to the quick-connect couplers, this will be the first step.)
I wish I could make the new "manifold" from 1" -- or even 1¼" -- pipe, but nobody makes "push" reducing tees that size, that would still have a ¾" on the side :( I would've had to install reducers, and I didn't want to increase the number of connections further.
A shame, really -- you could get a ¾x¾x½ reducing tee, no problem. But no wider ones...