First, I'd love to see what a "daft handlebar" does!! And comfo
Sorry about your injury! I've had a few, have needed physio, but no fractures. I did have one, but that was slipping on ice while just walking around!
It is definitely possible to raise handlebars, but your bike will have limitations. I'd also want you to avoid having to simply guess and buy a part, try it, buy another one, try it. As a technical type (professional engineer), my questions are really "how far up do you want to go?" and "how far back do you want to go?" Seems like you're in EU somewhere? If I were to help you, I'd put you and your bike on a training stand, have you assume the position you want to be in, carefully measure the new position and photograph you. Seeing as how you seem to still be under medical/physio care, I'd want you to use these pics to negotiate with your physio for acceptance of your target position, versus having to buy a real Dutch bike and upgrade the gearing!
To start, if you have a friend with a camera and a training stand, you can put the bike on the stand (level the bike by propping up the front with books), squirrel your body around until you have a decent position both for health and comfort, and take photos. Mark up the photos (photoshop or pencils) with the current positions of the bar grips and the desired positions of the grips. With that guide you can talk to actual bike technicians (or smart friends), and perhaps see if your bike is capable of the modifications you want. It sounds like there is a lot on your current bike that is good for you.
I think that is how to start.