Hi. It takes a while to establish a good routine but it's SO worth it! You said yourself that you're making progress! You can totally do it w/o CIO and you will feel so great when she's sleeping well and you know that you helped to teach her.
Your questions:
1. It's VERY common for babies to wake at that 40 minute point, esp when just starting a routine. FYI most babies outgrow the short naps as long as they can sleep independently and A times are appropriate. But for now, yes, go back in at 40 mins or just before she begins to stir and gently calm until she's back to sleep. This often works best if you get to her at her FIRST stirring before she wakes fully.
If she does wake, use shh/pat or calming method to get her back to sleep. I would not wait when she wakes early as she's not likely to go back to sleep on her own without help (she's had a bit of sleep and thinks "great, time to get up!"). You are not creating a prop by helping her to get back to sleep, she will outgrow the need for this intervention soon.
You can use shh/pat to calm, or a variation of it (some babies don't like the shhh or don't like the pat, you have to find what works best for your lo) and pick up only if she gets too worked up, putting down immediately when calm (if she doesn't calm after several minutes, put back down and work on calming in the crib, pick up again if needed). Your lo is still on the young side for pu/pd so I would avoid doing more than a few pickups, as this might overstimulate her.
DHs just don't understand do they?
BW mommies are all obsessed with sleep, join the club.
Once she starts getting the hang of this, you stop patting when she's quiet and settled, start back up again if she needs you, repeat repeat repeat. This way she eventually learns to go to sleep without your help. When you first start though and for the first couple of weeks of sleep training, you do pat for longer if needed.
YES, this absolutely takes longer to work than CIO but it's so much easier on both of you, and you're not breaking the bond of trust with your lo by leaving her to cry.
Good luck, focus on your progress! You can do it!