“My fear is screwing in the new barrel and having it bottom on the receiver”
Forgive, not my intension to scare, like reloading there is a minimum of tools required, then there is the technical part, it is possible to remove you barrel for the purpose of measuring the length of the barrel shank and case head protrusion, again, I measure the length of the chamber from the bolt face to the shoulder of the chamber first, after removing the barrel I measure case head protrusion.
There are times when someone decides they are going to order 3+ bolts in hopes of ‘getting lucky’ by finding a bolt to off set excessive chamber length of go the other way in an attempt to find a bolt that would increase the length of the chamber, that was never necessary, if the person ordering the bolts knew how to measure a bolt and could find someone with bolts that also knew how to measure a bolt, only one bolt would be required, then there is the little problem of finding a bolt that would off set the length of the chamber from the bolt face to the shoulder of the chamber.
You will have to decide if you are going to do the work, or if you are going to be able to find help or if you are going to have it done. Bottoming out on the front of the receiver is a matter of moving metal from the shoulder in front of the barrel shank or by truing up the front receiver ring.
I would not discourage you from acquiring a head space gage, I do not shoot gages, I shoot ammo, my methods and techniques make owning head space gages nice to own but not necessary, again, I shoot ammo.