Under 6 months I'd call the sleeps that happen in the evenings "naps". They would be where other daytime naps happen - in a bouncy chair at my feet while I sit on the sofa, in my case.
Unsettled evening at this age are completely usual. You're fighting a losing battle expecting anything else.
What would u do if u were me?
What I did with my 4 was:
Any wake up that occurs between 7pm and 8pm, I'd call that "bedtime". I'd do a bath folkowes by a massage and change baby from day clothes into night clothes.
Carry baby downstairs, feed again (I would have also fed upon first waking, before bathtime) and now that my other children are in bed, settle baby in bouncy chair and cuddle up to my DH for some much needed grown up time 
I'd bounce baby (with my foot) periodically, to help link sleep cycles. But I wouldn't expect it to be successful. At any wake up I'd
- first try dummy reindeer and bounce
- if not straight back to sleep, I'd feed.
At 3-4 months I'd expect a feed around 9pm and then whenever the next wake up happened (which I'd expect between 10-11.30pm), I'd carry baby upstairs, feed on my bed and put baby in cot. Brush my teeth and go to bed myself.
As we moved towards 5-6 months, I'd notice that baby stopped waking for the early evening (9pm ish) feed. It might mean that my bedtime becomes earlier, with a 10pm feed or so.
Over time I'd know that as well as not waking for the 9pm feed, the late evening feed would get later too. So maybe "bedtime" would happen 7.30pm and then baby sleep solidly in bouncy chair until 10.30pm, then 11pm....
Once it gets to the stage that baby wasn't waking up and I wanted to go to bed... so I was waking baby up to have to feed and take to bed... that's the marker I'd use for making "bedtime" mean upstairs in the cot at 7-8pm.
Once I knew there would be no wake ups between baby's bedtime and my bedtime. That has happened around 5-6 months old with my children. But I've know it take longer or shorter with other babies.
At that point, when baby was now being put upstairs early evening and staying asleep, I'd make a judgement on if waking for a dream feed is likely to be helpful, or not. It's not always useful.
In your situation I would have fed probably twice after "bedtime". Better getting feeds in while I am awake, rather than while I'm asleep. Any feed that happens after 10pm, I'd take baby to bed. Unless I'm knackered in which case of take baby to bed with me at the earlier feed.
I categorically would not be spending my evenings going up and down to baby.
Apart from that being too much hassle in my precious adult time in the evening, it's also against SIDS recommendations that baby should sleep in the same room you are, until 6 months old.