All work Visas is are very involved and costly for the company. The job that the company wants to sponsor you for has to be approved by the Dep of Labour. I can assure you from personal experience that with thousands of mainline pilots on furlough, they do not consider the labour force to be short of pilots in any way what so ever.
If anyone has given you the notion that just because there are only a few F200's around they will look overseas for recruits, they are missleading you. American companies consider a pilot to be qualified even if they do not have time on type. Unlike many other countries Americans will look at say a Hawker pilot and rightly consider them qualified to fly the F200 after sending them through a Type Rating either on the Aircraft or with say Flight Safety.
Good luck.... I sincerely hope you can pull it off as there is nothing in this world that compares to the opportunities of flying in the US.