I agree w/everyone else, if I had serious skin issues, making my own soap/body products would be so, so worth it. I have just regular dry skin - although v. dry - and using home made soap makes a huge difference. I made melt and pour soaps for a couple of years before switching to mostly CP b/c I was nervous about using lye, but w/good safety measures it is really not a well-based worry.
Also, if you do not want to make CP/HP for what ever reason, I agree with the others who suggested it, MP is much easier to do (literally just melt and pour if you are OK not adding fragrance and color, which would probably be a good idea if you have really sensitive skin), and a good MP base - I use the SFIC ones - is much more skin friendly than the bar that you are using.
SFIC bases do include a surfactant, but a better one that is in that bar, and only one. Additionally, there are a lot of other potential irritants/drying factors in that bar. You can also add a little bit of oil to MP (about 1 TB per lb of base) if you want to try the MCT.
ETA: Crap, I just re-checked the SFIC bases, they use a lot of coconut oil rather than palm/PKO. Although PKO is v. similar to CO (it is not like palm oil, despite the name) so maybe, depending on what the blend of PKO and palm is in that bar, you are actually OK w/coconut oil. I still thing it is worth trying, and buying a lb to test would not be v. expensive given the potential up-side.