On that pump there are two separate "zones" for oil. At the rear where the internal weights and controls are located, there is an oil sump. The oil in that zone is static and does not circulate with the engine oil. You check the oil level via the dipstick, and fill and drain via the same hole which is tricky.
The other "zone" is the front part of the pump where the plungers are. That is oiled from the engine feed line, and the oil flows back via a hole in the pump mount where it attached to the engine.
If the oil sump keeps filling up, it's coming from one of two paces. The seals in the pump can start to leak and gas leaks into the sump causing it to fill up. If this is happening the oil will smell of gas. The other possibility is that other seals are leaking and the oil from the front zone is leaking into the rear zone where it has no way out. If the oil does not smell of gas, then this is likely what's happening.
The solution in both cases is the same - send the pump out for a rebuild. It may sound scary, but it's no big deal and you will be very happy with the results. You could ship it to the US for rebuild (H&R Fuel Injection in NY is probably closest), but others can likely recommend a place in Europe somewhere.