In principle I'd advise against getting a second cat, especially while Tubby is still settling in, as (despite what the rescue centre might say) cats who aren't from the same litter rarely get along really well with each other (although some do end up forming very close bonds).
However, if you're confident that you can keep the two cats apart while they both get settled in, I'd say that you should go for it! You clearly understand cats far better than many humans do, so the second cat will gain a loving home, just as Tubby already has!
(I've loved reading that you're letting Tubby settle in at his own pace and that you're avoiding direct eye contact with him, which he might see as a threat. Another thing to try though is yawning at him! If you yawn slowly at a cat, while raising your head upwards, it will often be read as an "I'm no threat" message).