Firstly, the 7150 Plus can be calibrated from the keypad, iirc this is the entire reason for the Plus as the base 7150 is IEEE calibration only. If you do go for calibration, as another forum member discovered it is wise to check your chosen calibration service has the equipment needed to deal with 6 1/2 digit meters.
Secondly, your problem may not be due to calibration. If my understanding is correct every range has its own pair of calibration factors, the offset at 0 and the slope required to match the calibration value, y = mx + c. If the calibration is out on all ranges then all the factors are wrong, it's certainly possible that the unit was incorrectly calibrated at some point, its also possible that some common component has become marginal.
Thinking about your resistance tests. The meter has the ranges 2k, 20k, 200k, 2M, 20M, so your 100r resistor and your 1k resistor were both measured on the 2k range? The 100r was out by 7% and the 1k by > 0.75%, unfortunately '>0.75%' does not tell me a great deal but if 100r is out by 7% and 10 x 100r (1k) is out by approximately 0.7% there is certainly a pattern, possibly a constant offset? What does the meter read when the inputs are shorted?