I love the notion that one "termites" one's way into a subject matter, a business matter or an interaction. The images perhaps ghasts one a bit, if ghast qualifies as a verb form of "ghastly", but the insidious certainty of the term justifies the unfortunate mental image.
I always feel that the termite deserves the sobriquet "America's other social insect". Huge volumes by Harvard entomologists about the ants grace respectable bookshelves and sell well on Amazon. But nobody reads weighty tomes about "The Termites", except, of course, employees and relatives of the Orkin pest control company. For all their wood-chewing and disease-carrying splendor, though, termites work a hard day's work, and socialize well with one another.
So I write in favor of the verb form "to termite", because so much of human affairs is just one endless chomp-able block of wood, and we all need somebody who unobtrusively digs into the center, and makes the passageways out.