If the cracks have appeared recently and are still growing (in length and number) then this potentially indicates something serious.
Before you attempt any repair - which is perfectly possible using the method you outline - get someone in to have a look so see what might be causing them.
Have you put anything up in the crawlspace recently, or taken anything out?
Have you had an unusually wet or dry spell? This will change the ground conditions possibly causing the house to move which in turn could cause the cracking.
Mold goes away when the water goes away, so unless your toilet is leaking again, you have some other source of water or leak on the upper floor. This could be any number of things, even things not plumbing related, like water getting behind the siding, or a leaking roof with water running down the inside walls. As far as killing the mold that is there, I wouldn't waste my time. If you don't correct the water problem then the mold will return very shortly.
I need to figure out if there's still a leak or some kind of humidity problem. Is it safe to assume that because the problem got worse there is? Should I try to find the pipes and see if they're leaking?
Since you have had issues with the toilet in the past that would be the first area I would check. If the drain pipes for your upper floor are leaking then I would expect to see discoloration bleeding through the paint on the ceiling and the walls. If this turns up nothing then in the hole you have already cut, I would get a professional moisture detector device like the one a plumber would use.
These can help detect moisture and humidity in the air which can give you clues if you found the potential problem areas. Don't buy a cheap one because they don't work very well, I would instead see if a rental place will lend you a good one.
I think I'm seeing some black wood in there (need a better flashlight!).
This doesn't necessarily mean anything, it could be discoloration from previous water damage.
I would still like to hire someone to fix the plaster ceiling. Is it going to cost a huge amount extra if I cut through the mesh and they have to replace some of it? Does area make a massive difference in price for that kind of job? For what it's worth, I'm fine having drywall put up instead of plaster.
How big is the hole that you had cut? You can sometimes repair a hole by cutting a small piece of drywall and fitting that back in place, then using some thinset or spackle around the edges. Sand and repeat thinset or spackle two or three times until you have a smooth paintable surface.
Best Answer
If the ceiling feels spongy anywhere at all, some sort of deterioration has occurred. The most common cause is moisture seepage—whether from leaky plumbing, roofing, or pets—but plaster deterioration can also occur from sustained high temperature (120 °F/49 °C) as is common above an enclosed light fixture or electrical junction box carrying a heavy electrical load.
Decay could also be caused by certain pests like cockroaches, fleas, or larger critter's waste.
The first step to fixing it is to stop whatever is causing the problem. Then assess what needs to be done.
Wall and ceiling work is somewhat expensive if you hire someone to do it, but it is quite inexpensive if you do it yourself. Even if you don't know what you are doing and have to (re)do it four times, that will still be less expensive than hiring a pro. For a head start, visit your local Home Depot the next time they have a sheetrock demo. Or search for "sheetrock repair" on Youtube.
If investigation or repair require tearing down the ceiling, the price can escalate if you see something else you want to do: rewire, insulate, reroute plumbing, redo siding, etc. Frankly, the add-ons are the most difficult (financially and emotionally) aspects of such projects.