I did it a few times in my 13ft stabi 389! Shortest route from Mana (pretty sure it's okay to overnight your car/trailer between the bridges?), but I went through Queen Charlotte Sound out of the harbour, pick your day and it's a piece of cake, but it can chop up bad and quick, so always be prepared to sit it out and wait for a weather window (overnight at Furneaux etc.)... which can take a while sometimes.  If going via the South Coast, the Karori Rip is rather nasty and extends quite far out.  In good conditions you can do it in an hour or so from Mana or a couple from the SC. Coast to Coast - the sounds adds another hour or so.

Note: shadowing the ferry will put you into some clean water if choppy, but keep a safe distance.

Settled weather is March / April IMO. Take loads of fuel just in case... Your boat is more than capable. With a small boat, would not attempt it if Cook forecast is over 10 knots and .5m swell. Variable is best. Remember you're not crossing N to S, so expect wind / chop from the side / quarter do to prevailing N or S, seldom in between, although a light NE is sometimes good.

In the 90's I crossed Cook Strait many many times in my first boat - a Plylite fisherman.  It's not that far at all from Mana to Fishermans Rock or the Brothers.  A 6m boat is plenty but, as Flyfisher says pick your weather and head back straight away if it looks like cutting up.  I probably turned back 40-50% of the time because I wasn't happy with the conditions outside Mana Island but never had a really bad experience.

The time of year isn't as important as conditions on the day Quintana. Pick a period of neap tides rather than springs, and don't go if the forecast is 15 knots or more - there's plenty of fetch for the wind to get the sea up in both directions, & it can be pretty sloppy out in the middle even on a nice day. The worst of the rip areas are on the Wellington side from Sinclair Head to Ohau Point, but plenty of locals fish in those very areas so don't be too put off. A 635 is plenty big enough for the crossing on the right day, but take all the usual precautions, including a TR to Maritime Radio or local Coastguard.

Re slack water a tentative yes - the tides in Cook Strait are a law unto themselves when it comes to both flow directions & durations though.

Jase and Dave did it in Bumper Boats

I do it all the Time in my 5.6m stabi nothing to worry about 40 min each way mana- queen Charlotte

Don't over-think it mate, Pick the right weather and go, Tides etc don't matter.

5-15 knots in your boat will be fine. don't go in anything over that and don't go if its meant to get up.

and use common sense forecasts aren't always right so if your not happy with the conditions turn back.

Have fun

Hi. 

Hi. We are looking to leave from mana. What wind is the least troublesome?