How to eliminate clothing odor that seems to remain even after washing.?

I work outside a lot, and I live in Florida. In other words, I sweat like a racehorse throughout the day. Lately, I've been noticing that I start to really stink by the end of the day, where before it wasn't nearly this bad. I have very good hygiene, and I know my body's odor does not even smell like what I am experiencing. I am sure it's my work shirts. Although they start off smelling fine, the second I start to sweat they stink. I suppose I need to replace them since they are at least a year old or more, but they are like $45 each. I suspect my high efficiency washer may be part of the problem. It has a pretty small capacity. I've started making my wash loads smaller, but that's not helping. I've also tried adding products like Odo-Ban to the wash, but that just makes them smell strange and I end up with the same stinky result by the end of the day. Are these high efficiency washers just low performance? Is my body chemistry changing? Am I destined to smell like a sweaty old man at work??