I routinely make the residents do cases without midazolam and fentanyl. A few mL of propofol in pre-op to sedate the patient for transport works perfectly. Admittedly, the duration is too short for blocks, lines, etc., so periodic redoses are often needed. With regard to the poster who wants spontaneously ventilating patients with LMAs without fentanyl, I can't recall ever making someone apneic with morphine or hydromorphone (but I've seen it with as little as 100 mcg of fentanyl).
You'd be fine to give a few mg morphine or 0.5 or so of hydromorphone with induction and titrate from there. Personally, I don't give opiates routinely during induction anyway, so if it were me, I'd induce, place LMA, and THEN start titrating the hydromorphone, since they're already spontaneously ventilating shortly after LMA placement.
We were out of propofol for awhile, as well, and used lots of etomidate (mayb-i-date, as I liked to call it) combined with sevoflurane. Seemed to work okay, albeit slowly. And since vets don't puke, we didn't have a lot of fallout. 0.2 mg/kg seemed like an underdose, most of the time, though.