Leading minecraft cats deep underground, lava is preventing my several-thousand-block long self-dug shaft from being very straight at all?

I'm constantly plagued with random giant lava pools i must dig around, but since cats like to jump up on things, i do not want to risk being so close to the lava, as i have a small army of (use to be 13 cats, now its 3, most have been lost to their stupidity vs lava.

the tunnel i'm digging is 1x2 blocks, and many thousand blocks long(i've spent at least a days's worth of total time on this damn tunnel simply because the cats will drown if i try to drag them across the oceans between the jungle and my house. I'm a little over halfway done, and id love to know if there are better ways of going about this.

Yes

Dig long tunnels at Y-level 12, underground lava pools rarely spawn at that level or higher, and you still have a chance to bump into some diamonds.