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I understand your concern. You don't want your friend to be in pain but you would rather have your regular veterinarian come to your home. In my area there are several veterinarians who have mobile practices. You may have one that would come to your home to give that pain injection on Sunday, out of regular business hours and also help determine where your are with end stage decisions. There are also a few practices like Banfield who have some regular hours on Sunday where you might be able to make an appointment for an injection of pain medication or an evaluation.
Gabapentin can be absorbed well when given rectally. You would put on a glove and insert the dose in about 2 inches if possible. It will work faster if there isn't a lot of stool present. You would use twice the oral dose you are giving.