The club ride I presume is referring to 15-17 mph on the flats, not climbing. A 10% grade is a hard hill. Hemoglobin delivers oxygen to your body and helps it to remove carbon dioxide. This could well be the cause of your complaints, including "gasping" for air. But having said that, from what you describe, those are respectable numbers for a recreational cyclist. Most recreational cyclists aren't riding under oxygen deprivation. It might be worth getting your blood oxygen content checked while you are going full out on a trainer under controlled conditions, to find out to what extent this is a contributing issue.