Firstly, grey cards are not as accurate as your meter.
Secondly, depending on exactly how you use your minolta spot meter, you will have varying results. If you point it at the brightest part of the subject and use the highlight button, that will give you a reading of 2.3 stops brighter than exposing that highlight on the actual metered value. If you point it at the darkest part of the scene and use the shadow button, that will give you a reading of 2.7 stops less exposure than the actual value. Neither of these will be correct unless by chance. If you use the average function with with the highlight/shadow buttons then that will give the average between the two points which again won't be right unless by chance.

Your instructor was wrong. The zone system is as good if not better than other systems for very accurate metering and you have the meter to do it.
The highlight/shadow functions on the minolta are ideally suited to slide film which only has a scale of 5 stops. For B+W I would recommend you use zone system metering. Pick a shadow area in which you want full textural detail and meter from that area. That will be a zone 3. Then adjust metered reading by closing down 2 stops (see note below) and expose at that adjusted reading.

Note: As I explained in my earlier post, how much you close down to place something on zone 3 is dependant on what you have calibrated your film development to. i.e. a 10 stop range or a 7 stop range or some other range. In your case you seem to be using Ilfords figures for dev so I reckon your development will be calibrated more towards a 7 stop range. Therefore close down 2 x .7 stops = 1.4 stops or 1.5 which is closest doable exposure. You would close down 2 stops if you were sure your film was calibrated for a 10 stop range.
Forget about the highlights for now and just try this technique. The highlights will still be captured on film. You really need to do the print tests to determine exact film dev time.