travel cot with vibration in the mattress
Our bouncy chair has vibration, but I took the batteries out of it many years ago and have never used it with DD. I don't believe it makes any difference to sleeping (the foot bouncing of the bouncy chair does that) and I would become very worried about developing some sort of dependency on vibrating to sleep.
*since she's eating every time she wakes up, she's just very hungry
Are you sure it's not comfort sucking?
I hope your night with earplugs and formula helps tonight. Sleep deprivation is horrible.