I'm so sorry to hear that you're still struggling, and have had to stop singing. That is very tragic, indeed. I truly hope that you're able to find an answer to your problem and get thing back in working order soon.
Believe me, you're not the only one to find that during the PH monitor time their reflux suddenly disappears. It's very frustrating, I know.
Unfortunately, symptoms like yours (and mine) are less clear cut than plain wide-open LES and typical GERD. GI doctors generally aren't as knowledgeable in treating LPR symptoms like hoarseness or asthma symptoms. It took me 6 years to finally get a GI doc to listen and refer me to a surgeon. Once I'd healed, my lungs improved tremendously.
Still, if you're persistent, you can find help. I don't know anything about LINX or doctors in the UK. Sorry about that. Sometimes ENT specialists are knowledgable in LPR and its affect on voice. Keep researching and searching out answers. Don't give up!
Hang in there!