[GWN7]

If the house was built in 1927 it probably has no weeping tiles.

Is it a stone & mortar foundation?

If so, the water in the soil comes up against the stones and works it way inside.

As mentioned, sloping the grade away, extending downspouts, ect will help with the water but if you want to stop it completely you will have to dig down to the foundation. Clean the wall off. Put a weeping tile system in next to the foundation covered with rock. Then tar/sealant for the walls. Then waterproof barrier. More tar/sealant. Then backfill.

A newer home will have a connection under the foundation to the weeping tiles where the sump pump is located. This brings the water that is up against the basement wall in to the sump and it is then pumped away from the building. Expensive to retrofit but it can be done by concrete drilling a hole thru your footing below the basement floor grade and connecting the weeping tiles to your newly planned sump pump.

As this is your plan for the future

"I also hate to put a bunch of effort into the floor, because the long-term goal for the basement is to dig it down several more feet and add some finished space down there."

I would suggest extending to gutter drains and live with the water. Save your money and hire someone to lift the house and put a new basement underneath. It is a lot easier to do it right when it's all new than retrofitting.