I can't give you any specific advise because like you I am trying to figure out how to get a job in the forensics sector - and that seems to mean moving to America where scientists are appreciated.
What I can tell you is what I have found out from looking around the internet and reading various books on the topic btw a useful text is 'Living and Working in America' by David Hampshire.
It would seem that you need to apply for a visa - I believe the correct one is the immigrant visa which allows you to get work and move around the country. This is expensive and takes time, you may also need an immigration lawyer to make sure the paperwork is right as whilst you can apply more than once, getting it right the first time is more likely to impress.
Once you have that visa, you can then think about moving. Some companies will pay for you to come to America, or will help with shipping and set up costs on the agreement of you working a set amount of time for that company.
I don't know if that is of any help at all, I guess just keep reading and looking into the logistics is the way to go. You may want to consider applying for another science related job that does offer transfer assistance as they may be able to help with visas ect (I don't know this so be sure to check) or see if your current employer has opportunities abroad. Once you get there, get your green card and get settled then you can look in more detail at the forensics jobs in your local or chosen area.
If you wanted to get a phD in America there are several websites detailing opportunities for that but you should be aware that a student visa is likely to only last 3-5 years and you have no guarentee of getting a renewal at the end.
Please be aware that advise given in this reply is based solely on reading/research online and in books. I cannot vouch for it's validity and if anyone in American or who knows the system better wishes to correct information found here, please do.