Hi Jared, the Community hasn't spoken in response to your egg re heating time challenge likely because you have more experience than most on the topic but i hate to see your post just sitting there in its sorry state of utter reply-less-ness so here is a few link-free thoughts from the cat starting with give 135F X 10 a re heat try and wonder no more. if not warm enough well then a chef friend does eggs perfectly you know set whites and silk-runny yolks the way you like them at 63C about 146F for 90 minutes and then keeps them all day at about 80-90F which seems too low too me but that indicates to me that you could use that temperature without any loss of runny at home or you could do a flight of graduated test reheats at 5F higher with associated shorter 5 min intervals and report here for Community benefit your optimum time/temp discovery. of course if you are so fortunate as to have a thermoworks chefalarm with a proseries waterproof needle probe you can immerse an egg with probe inserted crank up the heat as high as you dare and cease re heating when the yolk reaches about 139F pull point which is lower than your cook at 145F but allows for carry over heating without diminishing runny it won't take long. Note the steady water temperature and immersion time and there you are. The whites will be a little more solid but who cares as long as you get runny right.
You might remember Nathan Myhrvold wrote extensively about eggs and has table 4.78 in his 2438 page Modernist Cuisine: The Art and Science of Cooking the only cook book i know that uses partial differential equations to explain cooking techniques but that would be a link too his egg re heat at 62C/143F for 25 minutes cat wont debate anything culinary with Nathan
Just don't re heat your eggs in the microwave.