Some cats are rather clingy, too bad you don't have the temperament for it. It was very kind of you to take the orphans in after your friend passed. I don't really have suggestions for you, but wanted to share my experiences. Your cat's probably going to stay clingy, so you'll have to think about what will make both of you happy.
My furrkids are all kinda clingy but Ginza is extra clingy. He follows me faithfully around the house 24/7, he needs to be in whichever room I'm in, we have scheduled cuddle times that can last up to an hour. He'll hurl himself at any closed door I'm behind, and he'll wail until he sees me. He'll spoon sleep with me, or shove my arm really hard at 4am to sleep under the covers over me or hubby. And we LOVE him to pieces.
You mentioned the more you shove him off, the faster he comes back. My Ginza needs constant reassurance from us, so whenever we see him we'll kiss him and tell him we love him, which seems to make him happy. Even when I'm in the middle of something and he taps me, I'll make smoochy sounds and tell him I love him, then he'll just sit still and watch me.
He's also the most intelligent and sensitive of my little brood. He understands "not now" when I want to be left alone to read my paper and drink tea. He'll sit still and wait for me to finish and give him a kissie.
If that sounds like yours, and you don't think you can take it, you've got some hard decisions to make. Good luck.