I found ~5-10 stones per 15 minutes in a house, this means that a 16 stone upgrade took on average half an hour to earn.
If you are taking half an hour to get 16 stones then I don't think you're exploring "effectively".
If you're looking for upgrade stones, you should only be looking for stash rooms (which you probably already are) and you should be looking at buildings where you are likely to have a good concentration of stash rooms and skip minor buildings and large ruins. You should also be looking at areas that would have good concentrations of said buildings.
There are other reasons you might want to actually go into the minor or large ruins and enter rooms other than stash rooms of course, but you don't need to for stash supplies like upgrade stones.
In fact, unless you are desparate I don't think you should be going on trips exclusively to get upgrade stones and other stash supplies. These should targets of opportunity you should be picking on your way to more important things, like secret missions, rare spell materials, and other important items. You shouldn't be going out exclusively to get these things.
none of the monsters in this game required any sort of thought or reflexes to avoid.
Your difficulty is probably too low in that case. You should either increase difficulty or in your case it might be better to start a new world using an "expert start" so that you start on the second continent with more content unlocked so you have more enemy types to fight.
The fact that you mentioned that the game is too slow to introduce new content also says you may be better off with an "expert start". That actually bypasses that problem, as you start with more content unlocked.
none of the monsters in this game required any sort of thought or reflexes to avoid. Platforms were way to abusive and cheap in AVWW, in terraria they weren't handed away for free whenever you healed, and monsters would occasionally destroy them. Terraria was also more enjoyable for me because you were one of the least mobile entities of that game as apposed to one of the most mobile in AVWW.
You're supposed to have lots of platforms. If you're getting them handed to you whenever you heal, then that also tells me you're not exploring effectively, because if you did you'd be getting more platforms than you would ever need in the process of getting your upgrade stones. (see above)
Platforms are in fact the slowest and least effective way to get somewhere. There are a variety of spells that you can get which will reduce the need for platforms.
You are very mobile in the game, but you're supposed to be very mobile in the game. Most enemies in the game shoot projectiles, and later on they shoot lots of projectiles. The esper balls you've probably already run into eventually start shooting multiple projectiles at once and much more rapidly later on.
It seems like excessive mobility now, but you'll need that crazy mobility later on to avoid getting hit.