erm no US psychiatry residency program is going to allow you to do a masters in psychology (which is a waste of time anyway) in this country! when you say during residency did you mean in another country?!
if you didn't do electives in psychiatry at US institutions as a medical student you would struggle to match into a decent residency program. When you graduated matters less if you have actually been engaged in clinical practice though some places have a soft cut-off of 5 years. Regardless, you might be advised to consider doing psychiatric training in the UK, completing your MRCPsych and then if you so wish, apply for psychiatry residency in the US. Also in the UK (which not necessarily helpful unless it leads to publications), you could do a diploma in psychological medicine or masters in psychiatry if you wished though the actual qualification itself may be of little utility it would be more relevant than a masters in psychology (which you may not even be qualified to complete at any rate).