As long as you can back up your lie with a grotesque amount of overconfidence, most hiring managers are not going to dig much deeper than surface level. Like you already said, they are probably overworked and just going through motions. Hiring you has the potential to ease their workload, not hiring you means wasting another afternoon conduction more interviews the next day.
The secret to writing a good resume is that people are lazy and HR departments are overworked just like everyone else so you can just fucking lie
10000000000000% this.
As long as you can back up your lie with a grotesque amount of overconfidence, most hiring managers are not going to dig much deeper than surface level. Like you already said, they are probably overworked and just going through motions. Hiring you has the potential to ease their workload, not hiring you means wasting another afternoon conduction more interviews the next day.