I know it is difficult (paperwork-wise) to get married while in Korea, but is it still difficult if you're stateside on leave?

First you want to ensure she is eligible to enter and remain in the US, if not a citizen. You can do this by her applying for a Fiance/wedding visa (may not be the correct title). If she clears this hurdle all systems go. Unfortunately there are times when things for. The past of foreign nationals unwittingly prevent their access to the US. It is worth it to do this right. It would be horrible if you married abroad and she was not able to enter the US. I have seen this first hand in Europe. Thank you for your service.

If she's American it should be pretty easy to marry stateside, if she's Korean she can probably come for the wedding no problem but the relocation would obviously be the harder part. If she's Korean Id recommend getting her permanent status footwork done first and then marrying her.

More difficult- faxing paperwork around the world does not do well- many thing used to have to be done in person- now you are talking official witness statements, etc.