Not cheap at all, that’s exactly what I do (only with a sledgehammer, not a jackhammer). Another viable option, if you have the proper resources and a high enough throwing skill (3 or better) is to:
Step 1: Activate and drop a high explosive (dynamite, C4, etc.) right next to the door, and run away. If using timed explosives, be sure to give yourself enough time to escape the blast. Wait for the explosion.
Step 2: Stand right outside the doorframe. DO NOT enter the building yet, the turrets are still online.
Step 3: Activate another high explosive (C4 does a pretty good job) and throw it in the middle of the hallway that leads to the stairs (this is where your Level 3+ Throwing comes in).
Step 4: Wait for the explosion. The explosion from the second bomb should have taken care of all the turrets, but if you are feeling unsafe you can always peek around corners. If there are any remaining turrets, leave and come back with smaller, more expendable bombs to finish the job (pipe bombs, grenades, etc.)