So far I've followed the following process with the spires.
1. Once located (using via caverns or Magma Sea) I approach and mine around the outside, proceeding up and down the column as well. Access to each spire has a separate sub-tunnel with some narrow bottlenecks, multiple doors, and usually a cave-in trap as an emergency seal. The doors are simply to slow things down and give masons a shot at walling things off.
2. On each level, once excavated, the vein is analyzed to see where the potential "clown vent" is. 1-wide "strings" can be mined right away, and probably were during the excavation process. Analysis may indicate that there in no chance of a vent on a given level. In that case the entire spire above that point is now safe to mine out.
3. If adamantine strands are still needed than a location is picked partway down a spire, smoothed, and then a fortification carved to check whether a vent is there. Said location is almost fully walled off first, and further precautions for quick sealing put in place. If the vent is not present; e.g. the 4x4 is solid at this point than the entire spire is safe to mine out above this point. (One sealing option is an obsidian mixer, which with luck might seal the vent itself as well as the holes just dug*.)
* - Two fortifications carved from either side at the same time. One has a sealed water reservoir ready to run through it. The other has magma. If a vent is there then open the two reservoirs and hopefully they mix well enough to make a seal.