hurleyreyes,
I was in this exact predicament at nearly the same age with my second child. I'll be back to help you prep for the week so let's check in daily even if we're in different time zones.
For now buy some medicine droppers or oral medicine syringes. We had to start on a different method for child to drink because he was too used to breast. It's a slow, frustrating process but when the choice is hungry infant/toddler or anaphylaxis you have to do what you got to do.
It's your call but I'd even go so far to start mixing Neocate with some breast milk now using a completely different method to ingest like a medicine dropper. You might start to think I don't know what it's like to have a 1 year old who has already anaphylaxed twice -- I have. First known reaction was blood in stool at three months most likely from my dairy intake that day. I went through weeks of Hemoccult cards making sure not even microscopic amounts of blood remained in stool during an elimination diet.
It's summer, it's hot. If 'all' that's happening with the breast milk is some rashing then I personally would risk mixing it now with Neocate and syringing it in small amounts and resorting to some sort of distraction like a toy (heck, TV under dehydration risk) interspersed with a solid or semi-solid you know he'll eat. I'd even mix it in with something like applesauce and syringe it -- anything to get that hydration and nutrition in. It doesn't have to be perfect... just enough to get through the next few days.
Neocate is formulated with electrolytes (according to our per) and the nutritional balance is such you won't get it in alternate 'milks'.
What is his menu like? Are there some jarred foods you can depend on along with snacks? Our list is at least as long as yours and we are largely formula dependent (as per Sinai dietician instructions) for key nutrients.
jarred sweet potato (no additives, read label)
jarred turkey, chicken
jarred apple or pear puree
^these can perform as an infant MRE short term, especially if you are short on time alone as a caregiver
I would take the time if you can to test out Ancient Harvest quinoa and quinoa noodles. Assuming child can have chicken (we are currently avoiding red meats until we can test) you can try browning plain ground chicken (read label) in duck fat. We use duck fat or corn oil for cooking to boost fat content per nutritionist's instructions.
Thus far we've also had good luck with Erewhon crisp brown rice cereal for self feeding.
Last question: Are you going to have any help while your wife is out of town? Will you be alone with child? And are there other children that you must care for at the same time? Hang in there.
Came back to add about Pedialyte. I'm no hippie but I'm one of those people who abhor the idea of giving a child artificial colors and flavors. I didn't even let my oldest child eat "safe" peanut free jelly beans until he turned 6. But an infant with dry lips with breast milk supply leaving town calls for doing the necessary, so grab some Pedialyte. My super MFA child has had it without issue. He doesn't like it but he's had it. If you start getting those dry lips and your back is against the wall use it to keep hydration up if things start heading south. You don't want to overuse it and check with your pediatrician for usage if you're unsure but best to have it on hand especially if the child has had diarrhea and vomiting in the past.