Hi there and sorry there wasn't a reply sooner...
It really does sound like it started with a growth spurt, especially since the NWs are at different times... meaning it's not habitual yet. When does he turn 6 mo? Just remember that along with the growth spurt, there are developmental leaps, too, that cause temporary night disturbances. Is he rolling to tummy? He seems to be eating plenty during the day and as long as your pediatrician cleared it, started solids is fine but usually best at 6 mo. (Helps with digestive issues).
I would not do sh-pat for longer than 15 mins... in fact, if he is not crying, I would wait 5-10 min to attend to him, then shpat for 15, then feed a few oz. if he doesn't settle. Growth spurt related NWs usually last a week or so, so we can see if anything changes around that time.
The increase in A time is a good idea and I would see how it helps after 3-5 days. Just keep in mind that if he is truly staying up for an hr or longer at a time at night, he may be more tired than usual during the day. So I wouldn't change it too drastic... perhaps only add 10-15 mins while we see if the NWs calm down in the next few days.
Like you suspect, we might be seeing the 3-2 nap transition, and the 5-6mo development all at once. The EW might be due to this. The increase in A time might help him have long 2 naps, as opposed to the 1 long + 2CN.