Not fun taking down the coroplast. Did it in a CG last year after the toilet decided to overflow during the night and soaked the insulation.
I would cut out only what's needed for access and slide it out in one large piece. Cut it left/right direction, not fore/aft. The sheet is unlikely to be a long single sheet and you may be able to remove screws that the factory used to join adjacent sheets and slide it out in one large section. You could add a piece of angle iron or aluminum between the I-beams to screw into.
There is RV "Scrim" tape for use on coroplast and Darco fabric or Gorilla tape is an alternative. Scrim tape is a lot thicker and has a backing on it that needs to be peeled off. Not sure if one is superior to the other. Both stick like snot to fingers, itself and anything it touches!
The insulation they use is batt type fiberglass. Not a good choice for a location like under a trailer. The slightest amount of moisture in batt insulation in it or compressing it greatly reduces the R-value. It definitely gets compressed between a holding tank and coroplast. You can buy rolls of batt insulation at building supply places or Ace hardware. Rigid foam insulation would be a better choice but harder to install.
A leak from the black tank could be from a number or reasons and you need to get full access in there for an inspection. If it's the ABS piping, that's easy to repair but if the fitting to the tank, that's harder to deal with and at worst, could require tank replacement. It might be something a simple as a coupling that wasn't properly glued at the factory.
Depending on where the leak is and where water travelled, water could potentially be outside of the I-beams where the outriggers are and you may need to slice the Darco fabric to get at the insulation.
While you have the coroplast down, it could be an opportunity to do other work under the trailer like wiring, adding an in-tank sprayer (if not so equipped), installing Horst Miracle probes, etc.