How can I time-switch a few loads very precisely?
Can this be done without oscillators or pulse counting stuff?

Yes, but it's going to be difficult to get the precision you want.  A circuit using several 555 timer ICs will do the job but you'll have to spend time trimming all your resistor and capacitor values to get the timing as you want.  But &quot;yes&quot;, it could be done.
If this were my problem, I'd opt to use a low cost microcontroller to do this.