Don't be too sure, I did the same thing, then switched back, and it started
fine with the original starter relay - so I put the A/C relay back, and left
it there - still had the same issue a couple of days later.
I wish it would stop completely, it'd be a lot easier to fix. Right now,
it only has start issue about once every other week.
Trailblazers have a a couple solid state relays that are famous for cracking. Loose low beams or the cooling fan control on the PWM signal.
The simple act of removing the relay and plugging it back in gets you a few more days as it pushes the crack together till heat cycles kill it again.
You may have the same issue swapping relays as the disturbance causes the relay to work for a few days again.