Why Killua didn't use Knov abilities? After watching episode 143 I wondered.
Assuming Knov also wishes to Gon full recovery, If Killua would contact Knov from the start he could use his abilities to teleport himself to Alluka and take her directly to Gon, or at least plan with him in advance to meet him on the road to the hospital and by that he will no longer needed to struggle escaping Illumi.
During all that arc, Killua is under the surveillance of his family and he is forbidden to show the abilities of Alluka or even talk about her or let people see her (e.g. a butler of the family interrupted a phone call where Killua could talk about Alluka, nobody except persons related to her family saw Alluka when she went in the hospital). If Killua disobeys them, Alluka and also himself will be forced to return at their family mansion.

Like you said in a comment, he could still have tried to cure Gon that way and return home with Alluka then but there are some points for which he can't let that happen :

1) There was still a risk that his family caught him before he cured Gon, so if he failed he couldn't help him anymore.
2) Alluka is the only member of his family that Killua really likes and she sees her brother as a good person so he doesn't want to disappoint her.
3) If Alluka was caught by Illumi, he would use the power of his sister for himself without caring about her. And Killua couldn't allow that to happen.