I have done this many times in the past. You have to wait for one to finish but there is no cooldown. Once the first service is used and once its completed you can “safely” use the other.
HOWEVER***** They are experiencing some SERIOUS issues on the “Character Transfer” Redemption side of things. I hope they fix soon as I’m the only one of our guild that couldn’t transfer.
All info about Character transfers is being updated via forum post here:
I sincerely hope you get the transfer to go through and you aren’t effected by the issues some of us are facing atm.