So sorry for your loss. It is a really difficult time for sure.
We had an orphan foal 2 years ago. Lost the mare 5 days after birth. We got her on milk replacer with a bottle and a lamb’s nipple. She did want want to do the bucket thing and because I was so tired, I just found it easier on both of us to keep bottle feeding her.
Hubby and I took turns and feed her every 2 hours around the clock for about a month and then it went to 3 hours. The first few days, we kept her in a stall with an open mare in the next stall. They bonded and we turned them out into a pen. After about a week, they got turned out into the pasture with the rest of the mares and foals. Godmare was great. 
Next door neighbour who was 4 named her Cinderella. Too bad it stuck as she then became the orphan. Cinder is now 2 and is as tall as her 10 year old sister at 15.3. I had her in at the vet’s when she was just a year old and he asked me how she was doing. He said he figured she’d be pretty pot bellied and fugly due to being a bottle baby. I told him that the horse I was holding was her. He was quite surprised.
We tried to do the igloo thing but couldn’t get an actual igloo brand cooler up here in Canada so I tried another brand. Could not get it to stop leaking. Cinder wanted nothing to do with the milk replacer pellets. We started her on a bit of grain after a few weeks and she did well all along. No issues with diarrhea, ulcers or anything.
You will do fine. Cinder would jump up at night when you went out to feed and would drink almost 3 litres in a feeding when she was older. As soon as she was satisfied, she went back to sleep. Out in the field, you’d call her and she’d run up to feed and then leave.
I only mixed about as much as we thought she’d eat in a feeding. Anything left was put in the fridge and then fed before the “fresh” stuff.
Good luck, and let us know how it’s going. It’s exhausting but so worth it. Friends kept asking me how we did it but it was so much easier than a human baby who would cry, need rocking, change diapers, etc. Plus they have the sweetest noses to kiss. 
Nancy!