I'm sorry to hear Calleigh is uncomfortable. If there is an odor, then I would suggest antibiotics. It is not unusual for tumors to become infected as they progress: this is especially true in an environment full of bacteria such as the mouth. Convenia is a good choice as it is broad spectrum and injectable so it generally does not cause any GI upset (nausea or diarrhea) like some other antibiotics can. One injection lasts 2 weeks. In addition to Metacam for pain, since buprenex is not tolerated well, you could consider adding Tramdol or Gabapentin. Like buprenex, both have the potential to cause sedation so keeping Calleigh indoors would be necessary.
I am not familiar with ifx.vet but did review the site and have limited knowledge of those kinds of treatments as they apply to humans. I did some quick research and learned from an oncologist that the clinical benefit of this therapeutic is not well defined as no peer-reviewed data is available to date. Also, this therapeutic is not currently approved or licensed by a regulatory agency. As a result, I would not recommend this as it could be harmful. I can see the argument for trying something "experimental" in the face of terminal disease but you would need to get your vet on board and accept the possibility that the treatment could harm Calleigh. I would not recommend radiation for the reasons previously discussed (i.e. stress, side effects and minimal increase in survival time). I would expect the response to be even poorer since the tumor has advanced. However, I would encourage seeing the specialist about further pain control should your vet decline to provide other options.
Continuing to socialize the kittens through feediing is the best way to get them used to humans. If they are hungry enough, over time they should allow people to get closer and eventually accept hand feeding. I would urge your neighbor to keep trying since the job is much harder as they get older. At this age, they will come around if effort is put forth daily.
Poor Jammie, he'd been doing so well with no coughing.... A half pound weight loss in a 17.5 lb cat is not very significant. Instead of your vet throwing his/her hands up, they should offer some options. I disagree that nothing can be done. His x-rays were suggestive of bronchiolar disease. I'd repeat them to assess for changes, but if the bronchiolar pattern persists, then a short course of oral steroids along with starting inhaled steroids (i.e. Flovent) is the next logical step since antibiotics failed. Having an inhaled bronchodilator on hand may be wise too (i.e. albuterol): however, this is not a stand alone treatment. I'd suggest taking him to the specialist ASAP. Coughing cats do need to be promptly treated to help avoid a respiratory crisis. You can read more about administering inhaled medication to cats here: https://www.trudellmed.com/animal-health/aerokat
I hope this info helps. Just let me know if you have other questions.