So I now have 6 females, and 2 big Ole males (neutered). It's no secret that I have a HUGE soft spot for the males. I kinda sometimes feel guilty that I kind of favor them (not on purpose). But my first heart rat was a black Dumbo, named Pepper. I was completely obsessed with him. Now, I have another black top eared, named Fig. I was totally caught off guard by how much he has filled pepper's hole he left when he passed. I've had other "favorites" throughout the years, but Figgy has totally pushed them out, and stolen the throne. I'm completely obsessed with him, and can't wait to see him in the mornings, and when I leave the house, I can't wait to get home and hold him. He automatically starts "chewing bubblegum" any time he sees me (his way of bruxxing and boggling), and comes running to the door for his hugs. He will lay his chin on my shoulder, and chew his bubblegum (actually tongue rolling, really fast), until I'm ready for him to hug the other side. Then, he will repeatedly put his nose to my mouth, so I can kiss it. When he plays, he will stop playing, to run up to me and get a kiss. Sometimes I have to give him multiple before he will run off again. If I'm by his cage, say, cleaning the other cage, he will lay on the side I'm on, and push his nose as far out as he can, cross his front feet, and chew his bubblegum. He's well...unique, to say the least! I have learned from the loss of my last true heart rat, to cherish every moment, and I fully intend to. Oh, and did I mention, he chews his nails? Seriously, I even got it on video! Omg I just can't get enough of him.....
I have yet to experience losing a rat, I've only been keeping them since January this year and got so addicted I now have 11 (4 pet shop does, 3 older lady rescues and 4 breeder bucks)! But I do have a few favourites, and one extra special boy with a huge/fun/sweet personality that I have a very close bond with similar to what you have described 
She also runs up to the edge of the cage when I come in and immediately climbs onto my hand and up to my shoulder. I love her so much and she’s almost 2 now so I dread the day I have to live without her. I have as close a bond with my rats as I do with my dogs and cats (with pepper it’s closer) but the short lifespan is so unfair. I try to enjoy every second I have with them because there is never enough time ❤