Oil pumps are not that costly relative to the price of your car or for that matter, your engine. If you bought a rebuild set '' cheap '' on the internet, that's what you have. Cheap stuff you bought that doesn't even fit. Those gear sets are made of
very hard metal and they won't be easy to work with.
Your oil pump doesn't create oil pressure, it creates volume. As long as your volume is adequate and your main and rod bearings are tight, you will have oil pressure. Even if you could fit those gears into the pump the pump body may still be worn and that can't be fixed. Get any one of those very fine tolerances wrong and you could damage you engine.
A high capacity pump, which is what I use, will allow for a bit more wear before oil pressure starts to go down. A good 113 engine will remain pegged on the gauge even at hot idle. However, as long as it shows full pressure at or before 1,500 RPM you should be OK. If your gauge falls below full peg at road speed you are
not OK. Either you are low on oil or you have
very worn main and rod bearings.
I won't back up a rebuild without a new oil pump and neither will any place that's worth your money.. Lots of fine broken pieces or grit can and do run through the oil pump if your engine is failing because that oil is not filtered before the pump. When, where, and how that happens is anyone's guess, but I won't take the chance of using a worn out pump. Neither should you.