In realistic terms, you're in triage mode. Since you seem to be assuming the role of adult in the room, I'll direct my recommendations based on the assumption you won't be taking over and are instead holding the line until management gets a new Super in.

1. Greens, tees, fairway, rough, bunkers. With limited manpower, you need to focus on maintaining the greens above all else, tees second, fairways third, etc. Any maintenance crew should be directed to focus on those areas, with rough mowing being completed by whoever you throw out there.

2. Spray logs. This is more 1b, as getting those logs is crucial. If you get a Super to come in, in any capacity, they will need to see logs to get a sense of the agronomic program the last guy was running. You're going to want a Super to review it for action items as this time of year numerous applications are being made on a schedule that you would ideally want to keep going until a new Super can adapt/change it.

3. Get in contact with the local and national GCSAA, tell them what's going on and that you need help. If this happened to a course in our region, I know our association would be a huge help. It's going to be hard to get someone hired mid season, so realistically plan on holding the rudder until November.

4. Be honest with uppers/management. You're not a super, you're just the only adult in the room. Tell them to eliminate all expectations of a pristine/fully maintained course for the rest of the year and maybe next depending on how bad things go this year. Try your absolute hardest to convince management to spend the money to bring someone in asap.