I have a clear bias here but-
I found daisy chain suspensions needlessly annoying for use with a bridge hammock.
I was always one loop off with no clean way to tune it up... in part it's also because you need to pull past to clip a carabiner (which then settles back and leaves you an inch per side longer than your clip point.)

So for me- I like a simple heavy webbing cinch buckle strap for beater straps. I got a pair with that REI chair thingy I bought on clearance that I've always liked.

This isn't quite right- but close.

There is a strap sewn onto the buckle that goes to the hammock (like half a quickdraw for climbing) and then you tension the buckle towards the tree. They have a much longer range of adjustment than a standard tri-glide since you don't need to open/close the loop.

I'm sure there is a system like them but since I sew all my own stuff that one I got with the REI camp sofa is the only one I am familiar with.