There is no need for A to persuade B to sever, as A can sever by written notice to B. The position would be the same whoever severs, but that won't help A. If severance occurs then A, B and C will hold as TICs as to 40%, 40%, and 20% shares. When B dies someone will take his 40% share under his will. If that is A, then A will be in the same position as if there had been no severance (i.e. he has an 80% share). If that is someone else, then A will be worse off, as he will only have a 40% share.
Of course A can ask C to give up their interest in the property. A disclaimer of an equitable interest does not need to comply with s 53(1)(c) as it is not a disposition. Or C could transfer his equitable interest to A using writing complying with s 53(1)(c). If C does either of those then A will be the sole legal and equitable owner. But this advice to A is essentially 'try and persuade C to give away 20% of a house'. He may as well persuade C to give him his life savings as well - why would C comply with either?