Integrating the sub(s) into the whole system is something completely different than finding a location for the sub to perform at its acoustic best. I would argue that you should do both with proper integration being an absolute must.
In my experience, I located two spots where subs performed well, I placed the subs in those locations, then proceeded to fine tune; integrate. I did move one of my Subs slightly after setting them in their original places.
Results were quite satisfactory.
Finding a proper sub location is part of the process of integrating subs into the whole system as no component is effected more on its performance as placement. The sub crawl works but doesn't work well and sub placement is better achieved through measurements rather than just listening by ear. As an example:
Below is my sub crawl result for my main system in the basement. The sub was located at the left of the left main speaker. Its response was becoming uneven across the listener position at 55 Hz onwards.
Results using measurements. Sub is located to the left of the fireplace and I found it to be much punchier.
I've gained 10 more Hz of flat response across all the listener positions and got a more even roll off for easier integration with the mains. I didn't have a miniDSP at the time as it was just a single sub. Without measurements, I wouldn't even attempt to try and place 2 subs. Placing a sub using measurements are far better and far more accurate than a sub crawl.