Can't really answer your last question, but the answer is maybe.
Assuming you have 7 cm above insertion point on your old stem, I think you have teh insertion line about 3 cm above the headset top. If you need to add about 5 cm above that to get back to your school-days position, you could target a new above-headset length of 15 cm. That is only available from a Nitto Technomic. Most people here will advise you to get a larger frame with an extended head tube, by the way. The technomic will then have an in-tube length of 22-15=7 centimeters. You really might have enough clearance in the steer tube for this to work as you expect.
It's usually recommended to make fitting changes a small step at a time. If you want to jump the whole 5 cm at once, the Technomic is correct. If you want to "inch" up to it (sorry), it might bottom out on you; I can't say. With a Technomic deluxe you can start with one cm above teh position you have and week by week scooch it up, giving a smooth acclimation period. Then when you really get the stem over extended (don't recommend it, but I have done this, too, don't tell anyone!), sell the Tech Deluxe and get the Technomic.
Another thought is to have your position checked by a good fitter and get some advice on what might be the causes of your hand issue. It could be height combined with reach, or maybe something else.