Here is what I think.
I'm an MD (fellow in medicine) who went to a well known US school.
If you look around at the hospital where I'm doing fellowship, you pretty much can't find a Caribbean MD. I'm not saying there are none, but there are very few. You can find some foreign medical grads, but mostly foreign people (i.e. born and trained in India, etc.) or a few Europeans. There are quite a few DO's (US students/citizens of course). Going to a DO school does make it somewhat harder to get residency in an allopathic (MD-run) hospital, but depending on the field you want to pursue and the hospital, it can be done. Also, DO's have their own hospitals and their own residency programs that they run, so you could choose to do residency at one of those (or at least have that as a backup). The US MD schools and DO schools have increased their enrollments the past few years, which has (and will) probably make it harder for US citizens who went to school in the Caribbean or Europe to get a spot in a US residency.
I think that it is worthwhile to consider all reasonable options at this point. That might include considering other health care careers (physical therapist, PA, MPH/health policyt, etc.) as well as considering a DO school, or one of the better Caribbean schools, or an Irish or UK med school.
I do think that a lot of the DO schools put not as much stock in the MCAT or having a really high GPA, but they do tend to emphasize clinical experience. That means you should try to make sure that your volunteer hours and physician shadowing are up to snuff if you want to apply there. Also, schools do not want to be someone's "backup" so you should be able to state good reasons for wanting to go there. I think that the DO schools vary in terms of their quality, maybe more so than the US MD schools. I've worked with some interns from one of the DO schools, Western U, and I was impressed with them. There are a number of other schools that seem like they have pretty good track records as well. One thing I think that you should try to determine (hopefully before you apply, or if not then if/when you get an interview) is how well do they do with placing their students in residency (DO and MD). They should be able to produce a list of where all the past couple years graduates have gone on to train (and in what fields). Ideally you would probably like to see that people didn't match into only a small number of hospitals, and didn't all match into primary care (nothing wrong with primary care, but if almost all students end up doing that then it suggests maybe some didn't have a choice of what field they ended up in). The school should be able to show you that they have strong affiliations with training hospital(s) - ideally you don't want to end up being farmed out (during 3rd and 4th year of school) to a whole bunch of different hospitals, that may be far away from the school. I think at schools like that the teaching tends to be haphazard, and the students' education suffers.
I think if you are considering DO then try to find some recent DO graduates to give you info on the strengths/weakness of their schools, just like you would do with MD schools.
What do you think were the problem(s) in your application that are keeping you out of med school? How do you think you can improve on those?