Day 3 - about to start - my thoughts
Sri Lanka should be able to get the last NZ wicket early... though it is possible for a final wicket to remain, dribble on for hours.... annoyingly.
IF needed SL can take a new ball in an over and a bit (after 80 overs).... new, hard ball, bowlers fresh first thing in the morning... look out tail-end batsmen

They should end with about a 50 run lead? Having a lead is a psychological plus, but 50 runs either way is no big deal really

Anyway.. as I said already.. the two second innings will (of course) determine the match outcome. As always ( in NZ) weather could interfere? So there needs to be some attention to getting on with things.. ya never know if RAIN will steal a few overs, or even a whole day

Sri Lanka should bat like hell all day today and into tomorrow. IF they were to declare it would only be with a lead of 500+?
They do need potentially more than a day to bowl NZ out.... I would say.. declare and put NZ back in early tomorrow... so they do need to get a move on and score a few runs today
From a NZ perspective:They need to bowl like they actually HAVE a bowling attack!!

4 or 5 wickets in the first session... knock the rest over after lunch

(maybe a short time after tea. Get SL out with their lead <300 Then get in and bat themselves with 2 days+ to make a target ( around 300)... not a big ask NZ has always had good top and middle order batsmen ( apart from Taylor).. and a tail that can bat OK as well.. 300 - 400... easy peasy.
Speaking of Taylor.IMO he is past his use by date. I know he has good record and all, and is a "senior member" bringing experience to the team, but he fails more often than he succeeds.. he is simply out of form (or past it). He is in the team as top batsman only and he is failing at that job. NZ has never been short of good middle order batsmen.. there are a gaggle of them around now playing 1st class cricket. A few of them NEED to be given a go at test level... take Taylor's place. If they "fail" then nothing lost since Taylor fails most innings anyway... and at least the new player will likely be a young guy a bit more athletic in his fielding than Taylor.. Gnomesayin?
Taylor will be retiring in not too distant future, as will McCullum.. all the more reason to "blood" a few new batsmen at test level.. have a few "in stock" as it were.. with some test experience.. who can be brought in to replace Taylor and McCullum when he goes.