We seem to be going down the same road as you lately:). When I stopped nursing to sleep, I did a short nursing session in the living room and then took them to their beds and told them, "time to sleep, close your eyes and go to sleep", and they did! Just kidding. I did tell them that and they cried and fussed but I was DONE nursing to sleep so I just patted the one I was putting to sleep until she slept. It took one about 30 minutes and the other went pretty quickly. It got easier each night. I do have a husband who does one but I have them alone a couple nights a week and for naps. If alone, I will usually put the easier one to bed first, she sleeps in my bed, while my son plays with the other one...then I put her in her crib (she is the only one who will sleep in the crib) and sit with her until she drifts off. If it isn't working for some reason, I will just put them both in my bed and do the same thing and just separate them with pillows so they don't end up in a pile. It was sooo much easier than I expected it to be, mine are 20 months btw. It is a huge relief to me because they sleep much better now and I get some free time without the frequent wakeups and having to nurse back to sleep.
So, to answer your question, I would change their beds and go for it the same night. Just be firm and do not give in, continue to tell them to go to sleep and resettle them for as long as it takes. I would just sit between them or at the foot of the bed. Mine didn't seem bothered by the others crying which I found odd because they have never cried at night since I have always co-bedded all of us and nursed them whenever they wished. It really was more difficult for me because it went against my natural instincts but I was going crazy having TWO babies that wouldn't sleep without me.
good luck to you, I hope you have a smooth transition and get the results you must be needing.....