In very broad terms, the CAA medical determines the state of your eyesight now; hence the retest on a regular basis; so, it's either good enough, or isn't.
NATS (& any ANSP) will be more concerned with the prognosis for the future; hence why the decision will have taken more time & more discussion. They're looking for a period of employment as recompense for the investment they're making in your future, &, sadly, they've decided that at 36, with your eyesight where it is, & the projection over time of where it's likely to go, they don't think the benefit outweighs the risk.
You could invest in the training yourself, get a licence & apply to any employer, but, very few are actively recruiting at the moment, & therefore your investment may not pay off. There are time criteria regarding how much time you have to comence unit training, following licence training, it's not long. You'd be taking a pretty brave leap into the unknown in the present market, I'm afraid.