How do you block off the big ring?

whatever you do, don't try and just lock off the mech in the smaller chainring without slackening the cable. It's easy to wreck the mechanism of a sti type lever by trying to shift it into a position that the cable travel won't allow.

I found this out the hard way when using a triple lever on a double setup. The bike is now running as a 1x9...

if you just want to use the inner ring and the limit screws don't go in far enough you could just shift into big, undo the cable and the mech will fall back to the inner position. tighten the cable clamp up again and you won't be able to shift even if you want to.

The limit screws do not affect cable tension at all. If you only want to use the inner rings, you would just fully screw in the outer limit screw (normally marked H, sometimes located on the inside) to prevent the mech shifting up to the biggest ring position.

The cable tension should still be fine for the inner and middle shifts, but you will meet some resistance if you try to go further. If you are struggling to shift into the middle ring having done this, you would need to back it out again slightly.

I used my mountain bike as a 2x9 bike by removing the biggest ring and just turning the outer limit screw in sufficiently. It should work fine.