Have had two out of three sons with reflux. First was the normal type, second was 'silent' reflux (guess that is the same as hidden) and was only diagnosed when he was having tests for something else. With first I stopped feeding at the breast fairly early on but express fed for 5 or 6 months (and worked 3 days a week). With second, he fed at breast a bit longer but then express fed for about 4 months (again working 3 days pw). With both, I found they did not take to having their medicine separate from the milk (ie mixed with milk and given by spoon/syringe) and as I did not want to give up b/f, I expressed and mixed it in bottle. It worked, but was hard work! I did know other b/f mums who managed to continue feeding at the breast because the medicine given by spoon/syringe worked fine for them.
I suppose what I am saying is different ways work for different mums/babies. None is less right. If you want to continue b/f either at the breast or expressed, then do so. I was like daisy the cow with number one and could have expressed for two or three, with second it was harder.
First son spent most of his first three or four months sleeping in his car seat as that was the only thing in addition to the medicine that lessened the discomfort of the acid. Raising the cot is helpful but we found the car seat to be more effective. He didn't seem to mind in the least and was not overly wakeful overnight.
Increasing milk supply - no suggestions other than sometimes you can drink too much water and this can reduce supply. Also, if the whole situation is making you uptight, this can also effect supply.
You seem to know what you want. Try to relax, plan as much as you can the b/f or expressing. Sometimes a change of position when baby is latched on can also help lessen the effects of reflux (can't remember exactly what now - something to do with reducing the speed of the intake, if that makes sense).
It is possible to get through the problems you are facing and you should get lots of support (and heaps more useful info) from mums on this site.
Be strong, take on board what advice you think will work for you and well....go for it!
Best wishes.
butterfly
(oops, sorry reply turned out long)