First of all, all soaps that will be used on body or face need a minimum 4 weeks of curing, I personally do 6 weeks at least. Most soaps can benefit from a longer cure time. For my facial soaps and salt bars I will cure them for 3 months. If by short cure time you mean less than 4-6 weeks than you'd be better looking into MP soap or syndet bars.
You said that you will use a lot of essential oil in the soap to make it therapeutic. But please be aware that all essential oils have a safety range. Adding too much could be bad for you instead being beneficial.
No matter what recipe you use the essential oil you used will always be somewhat damaged by the lye, no way to avoid that as long as you are using lye. Lighter EOs like citrus will pretty much disappear to nothing after a long cure from my experience.
With these questions out of the way, if you want a harder bar, you need to add hard oils/butters to your recipe to make a harder bar such as lard, palm, tallow, cocoa butter, shea butter, etc. 100% olive will need months, or even years' cure to make it hard since olive is a soft oil.
I understand that you want to use your soap as soon as possible but curing soaps longer can also make them harder. You can try use a water discount when soaping. Using less water can make finished soap harder.
Adding additives can also help. Sodium lactate won't make soap harder than it should be but it can make unmolding easier. Adding sugar or sorbitol can help lather. Adding salt can make bars harder, etc.
). But I'd like to investigate a bit more..
