Prayers going out for Ash! I hope that the vet can find out what is going on. Hopefully nothing serious.
I know you mentioned that the syringe you use to give him water is small but I've also found that if I squirt too quickly I've caused my cats to cough for day or two. Maybe it's this? Hard to say so it's good that your taking him for a full check up and bloodwork.
Maybe the vet will allow you to administer sub-q fluids to Ash at home each week. That way you can get a 100mls in him in about 5-10 minutes.
Hope all goes well with the whitecoats!!!