"I wonder if there are any predators that can be encouraged."
Birds and toads are your best bet. I'm blessed that I don't have squash vine borers to deal with. Plenty of squash bugs here but no borers in my garden(s). A lot of my customers have the borers though and for those that plant early I recommend row covers (and yes, I saw you don't like using them, Dave, but Wait! There's more!...) (love that cliff-hanger! *grin)....
Around here I watch for the chicory to start blooming. If you have it in Texas keep an eye out. When the chicory flowers the adults are out of the soil and flying around, looking for suitable egg laying areas, your squash or pumpkins. Those that want to use row covers should keep the plants covered for a few weeks until the flowers come on, then pull the covers off so they can get pollinated. If you like, and have a small garden you can replace the covers if you've seen plenty of bee activity. If you have time and patience you can hand pollinate and replace the covers.
Dave, if you're doing a huge field of pumpkins there is no way to row cover it. I have no idea how long your growing season is but folks here have done well planting a later crop, July-ish or so. By then the adults have quit laying and your later crop will mature fairly bug-less.
If you're growing squash then you might want to stay with the solid stemmed types until you get the SVB population down (may take a couple or 3 years). Butternuts and most melons are the least affected by them since they don't have hollow stems.
For those of you willing to dust or spray, Rotenone is considered "organic" but I encourage folks to not use it due to research showing it has a role in contributing to Parkinson's Disease symptoms in humans and is also a "bazooka" in the garden, killing many beneficial bugs, the last thing you want.
Oh yeh, birds! I have an abundance of birds here, having always encouraged them by leaving plenty of natural weeds/flowers/shrubs/trees etc. My bean trellis posts are cut so they have "perches" on them; it's a great treat to see bluebirds, wrens, etc, in the garden, swooping down and grabbing a bug and carrying it off. Bluebird will even snatch bugs out of the air (think adult SVB moth). As for on-the-ground patrol, toads are the go-to creatures for that.
Shoe (once again getting entirely to long-winded)