My guess would be that if he is coping well enough it may not be worth following up on the silent reflux question. I'm trying to remember when mine started meds, it was lateish, I think around 5 months, and would have been almost 6 months by the time I'd argued enough with the GP to get an appointment with a paediatrician. I'd suspected for several months but he was coping, then suddenly he wasn't, although in hindsight a lot of the trouble we had with sleep from around 3.5 months to 5.5 months was likely related to reflux pain

For me it became very clear that something needed to be done all of a sudden when he brought up a lot of milk (unusual for silent reflux) and was clearly unhappy. I wish I'd pushed much sooner tbh.
I dot' know where you are but I do know the 'paranoid mother' approach, I'd been mentioning problems for months to the health visitor, it was only when I demanded a ped app that we got somewhere. Within 5 mins of walking into the peds office she had diagnosed silent reflux and prescribed meds. It astounds me that GPs and HVs ignore these problems in babies.
So, don't know what I can advise, only what I said, if he is coping ok, not in discomfort and the only thing is taking more milk at night then I'd likely not push, on the other hand if you feel there is discomfort or pain, sleep problems, back arching etc then I would demand a ped app and seek some meds. I didn't like my LO on meds but the long term effects of unmedicated/uncontrolled reflux scared me.
Starting solids can go either way I think. Mine took to solids eagerly (I planned to wait until 6 months but he was so eager I couldn't hold him off past 5.5 months). I did BLW so there was not a huge amount of liquid going in, maybe the solid finger foods helped. But I also hear of LOs having food aversions from the pain they have experienced with reflux, and reflux babies sicking up puree. Maybe a thread on the reflux board would help you get more experienced eyes than mine x