There's confusion about the Chama regs.
Launch reservations are in demand only for weekends. If you win a lottery launch, it's for a Friday or Saturday putin. Summer dam releases are usually from noon on Friday to noon on Sunday.
Weekday launch reservations shouldn't be hard to get and I don't see anything about having an application on file before you call here:
Rio Chama Wild and Scenic River
The river usually has a spring runoff that makes weekday May trips doable. June and definitely July and August weekday runs aren't likely because the dam won't be releasing.
I've done both April and September trips with good water when you just showup at the putin.