You sound like a prime canidate to me, but it sounds like you have a couple years wait until you can see for yourself. I also had terrible razor burn with the cartridge razors even to the point I though I had sensitive skin. Since switching to str8s I dont get razor burn most shaves, it does take some time to get to that point, until you relax on your technique and the burn comes back to remind you not to do that anymore.
You might be able to find a middle ground with your parents and get a double edge, that way you can work on your pre-shave prep, for that matter you might just use str8 type soaps with your cartridges and practice that way. If you incorporate mapping hair growth into your cartridge shave your shaves will probably get a little less irritating. Since moving to str8s I found that the spots where cartridges were especially irritating my hair grew in different directions and I bet if I would have switched my shaving direction with the cartridges they might have been better shaves. That knowledge is for not with me now since I never see myself going back to cartridges, but it might help you until you are able to make the switch yourself. Spend some time in the wiki and browsing the forum then when the time comes you will be fully prepared.