Hmm, tricky.
If he is now on a 3hr E but you are offering a 3hr A he doesn't get a chance to S before being hungry again.
Most 4 month olds are moving or have moved to a 4hr EASY. Can you gradually extend his E times to 3hr 15 for a couple of days then 3hr 30 for a couple of days and so on until you have a 4hr E. Even at 4hr E with a 3hr A he only gets chance of a 1hr S before being hungry again, but, he 'should' be taking in more at each E and able to last the 4hrs. We might be able to look at a top up before a nap if needed.
The crying you describe sounds UT, I'm going to assume he is a very alert and inquisitive LO
Maybe look (and record for yourself) what sort of activities you are doign during his A time, for instance does he have lots of floor time or is he in the stroller/bouncing chair a lot, does he get lots of mental stimulation with books, toys, blocks, musical instruments/rattles. There might be a way to tweak his stimulation level to make him physically and mentally tired and ready for a nap - whilst not over stimulating which will prevent him relaxing well to sleep. For now just record for yourself what he does so you can begin to see any patterns. For instance if you take him to a baby swim class this would tire him physically sooner than if he is in a bouncer watching you fold laundry (which is still a great activity but not the same yk).
Can you pop in to him at about 25 min and do a W2S to try to get him to nap longer than the 30 or 40 mins? Pat him through the transition and into deep sleep so he doesn't get a chance to fully wake.
With the NW if he is just babbling and not calling/crying for you it's fine to just leave him to it. Tracy said LOs often wake at night and will eventually put themselves back to sleep (if they can and if they are not disturbed which can make the NW habitual or the resettling a prop).