The oriface tube is in the smaller liquid or high pressure line. The working of R-134a is dependent upon the condition of the components of the system, that is the A/C compressor, accumulator/dryer, oriface (a type of expansion valve), evaporator core, and condenser core.
A system does not care what kind of refrigerant it has to work with. The efficiency of the system depends upon its condition, not the refrigerant.
So, you can have a shop evacuate whatever remains of your original charge of R-12, replace the oriface line, and recharge the system. But, at $225 to $250 per pound for R-12 this may not be a good economic choice.
The oriface line can be purchased for about $40. A conversion kit with new "O" rings that are R-134a compatable, new garter springs, and about 8 ounces of R-134a oil is about $35, and about 30 ounces of R-134a, and you can do a conversion(R-123a is about $10 to $15 per pound.)
However, it would be best if you remove the condenser and have it pressure tested and cleaned. The accumulator/dryer line should be replaced, and the compressor should be removed and drained of its R-12 oil. Do not try to clean the compressor. The compressor should take no more than 84 inch pounds of turning torque to spin it in a clockwise motion. This test applies too a compressor that has been removed and is not under pressure. (I just know somebody is going to try this with a compressor installed and pressurized!).
The crap that has your oriface plugged up is mostly from wear of the parts of the compressor. If the compressor turns freely as tested above, then it should be OK for continued use.
When everthing is back together the system has to be vacuumed. Do a search and read about the process in one of the many prior posts.