It sounds like you are getting some longer naps in the cot than in the swing, which is really good work already, and like Shiv has said the mornings are definitely looking better.
I think at this stage (and with it being early days and no paed appointment yet) I would go with the line of least resistance. If you prefer to get them a longer sleep and the cot sleep does that, even if it means they might be sick and you have to clean up all the time, then go with that. If you are finding it even more exhausting to be cleaning up all the time and they are not sleeping that much better in the cot than the swing then why not stick with the swings if they're sick less often that way. Whatever you need to do to get through I think.
I was also going to ask if they are on any thickener, this did at least make a bit of difference to us with the sickness.