Proper conditions for a sump?

I'm working on a house with an unbelievable mold/fungi issue cause partly by closed vents during a rainy month, a city hydrant that ran for four months at the property line saturating the ground, and no gutters.

When I first started tearing out the floors and joists I noticed it was pretty damp even though it had not rained recently. Mushrooms even grew in one area. I opened all the vents and with the open floors and a dry month, the ground dried out. House has obviously had floor/moisture issues over several decades indicated by the different repairs I found. Decided I would install a sump well/pump to prevent future issues along with a vapor barrier.

Finally got around to digging the well hole and I'm not sure if this ground is suitable for a pump? First for 4" dirt, next 4" sandy soil, then very hard red clay.

My question is if water will even be able to flow to the sump well. With only 16" of clearance, putting in drain tile system isn't very feasible, esp with this being an older, low value rental property and having a professional company do the work is not in the budget for the owners.