To improve the cooling effciency you must stop the hot and cold air from mixing. The only way to do this is by designing hot and cold aisle and putting blank plates in the unused space in your racks. This way the cold air is pulled through the servers by their internal fans. .
Rack shitfing is most likely your only hope to get hot and cold aisles. If you do not address this now it will only get worse. The expense of doing this move may be saved in your electric bill but for a true ROI you must do hot and cold aisles and move the cooling closer to the load. In some US states the government is giving rebates to companies who make their Data Centers more efficient.
If you have a sealed room (walls to the deck above) with a raised floor and ceiling . I would use the ceiling as a return plenum to your AC systems and put open returns in the ceiling of the hot aisles to move the hot air out. Both APC and Liebert make AC systems that can do this.
To answer your question better I would need to see a floor layout.
NE Harris Assoc, Inc.
Even if you dont want to buy the new racks, you should prepare a plan for laying out the existing hardware in a hot/cold manner, and then use that as a master plan to work in during various outages and you will ultimately get there.
Regarding the fear of ”what if a few servers just refuse to wake up after the shift?”, you need to be ready for that. What if some server went down today due to a powerspike or got too hot or whatever? What are your plans for thaT?