It would be worth the $123 for me. I did fly with my kids when they were infants without a ticket but took their car seat and if there were empty seats on the plane they would rearrange and let you use it. My understanding is they don't do that any longer and I wouldn't want to do it knowing I would have to hold them, Also the flights I was on were less then 1 hr so worth the risk it was worth the risk of no empty seats.
All the safety reports support not holding a child, people have died in airplanes from turbulence, a child is expecially at risk and as much as you believe you can protect them you it would be difficult to hold him if air pressure was lost or you hit an air pocket.
Children are used to being in their car seat and he may even sleep. You and he would be in for an uncomfortable flight if you don't have the option of putting him down for part of it.