No need to go through all of this.

OP cannot add his KTN to a JL ticket because JL does not participate in Pre-Check.

As to any US domestic carrier, you may simply find your reservation online on that carrier's website and enter your KTN is the proper field in your passenger profile. You may check in online, print a BP or use the carrier's app if you wish. No need to waste time standing in line for a new BP which may not always be possible.