I just thought I'd follow up on this because I JUST NOW finally did this. The script is as follows:
M140 S102
M105
M190 S102
M140 S112
M105
M104 S240
M105
M109 S240
It works great! The only issue I have with it is that when it runs M140 then M104, it only shows updates on the extruder temp. The be is increasing to 112° in the background, so it works as intended, it just doesn't update. I threw the extra M105 in there hoping that might do it, but it doesn't seem to have any affect. I'm ok with it as it, but if anyone has fix, that would just be the cherry on top :)