Yes you can definitely make it from Mt. Sinai to Greenport in one day and it should only be about 9 hours. I did the reverse trip from Greenport to Smithtown which is further west than Mt. Sinai and I think it was 11 hour total.
Also Greenport is a really nice little place to stop. I don't know when the last time you were there was but a couple of years ago they built a very nice town marina with floating docks and great facilities. It is located right in town with less than a minute walk to some great restaurants, bars, shops and marine stores such as Preston's.
Marina link: Greenport Village, Long Island, New York
You would have to round Orient Point but I would suggest passing it and going in further to Greenport as there isn't much to do in Orient at all - really just a residential area with a ferry and a restaurant or two.
You do still have to worry about the tides/currents going from Greenport to Block as even though you are not going directly through the Race or Plum Gut you will still get 2.5-3.5 knot currents on either side of them for quite some distance. However since the trip from Greenport to Block is only about 7 hours you can really use these currents to your advantage. Just leave at slack tide and you will have 2-3 knots of current helping you along the entire way. I did the trip from Block to Greenport 3 years ago in my first boat - a small 25 ft day sailer and after the first hour we did an average of 7.5-8 knots over the ground the entire way to Greenport(the boat only did 5.5-6knots over the water).
Mattituck inlet is another nice option if you are leaving from Mt. Sinai. When we go we usually leave Friday late afternoon (so we get an extra day of vacation after work) and with an ebbing tide we make it "dock to dock" to Mattituck in 4 hours. The inlet itself is very pretty and very quiet and almost feels like a small river down south. At dead low you have about 5 feet of water at the lowest spot so if you draw 5' or more you may want to time your entrance. The inlet winds back and forth for about a mile and you have three options - anchor all the way in the back where it opens up into a little circle. It is very pretty back there but can get tight with a lot of boats making the same stop over point. You can also dink into the marina right there and there is a very good but kind of expensive and fancy restaurant right on the green there. Your second option is to stay at the Marina there which is called Matt-A-Mar Marina but I would make reservations in advance and it can be expensive. The third option which we did last year and really had fun was half way down the inlet there is a kind of run down red building with a small dock attached to it. This is actually a pretty good restaurant that you can sit in or outdoors and get some good and relatively inexpensive food. The dock continues next door where there is a real small marina with a side dock to pull up to. Late afternoon and night no one is there so you can tie up, get dinner and leave early the next morning before anyone arrives all for free. If you want to stay in the morning for a little you just pay the office $40.
If you stay at Mattituck it is really important to time the tide and if you do it right you will rocket to Block in about 7.5-8.5 hours and even getting up to 10.5 knots over ground going through the Race. If you time it wrong and leave against the tide you will be doing 2-3 knots over ground for a good 6 hours. The currents are just really strong in the eastern part of the Sound even when you are not near the Race or the Gut but again this could really help you if you sail with them.
So sorry for the long post but I am sitting inside with snow all around freezing my butt off and thinking about this stuff is the only thing exciting right now lol.
Where do you usually visit in the Sound when you come up? How long have you been coming up here? I sail my Morgan 323 "Capricorn" out of Mt. Sinai and my fiance and I usually travel to a different part of the Sound every weekend whether it is CT or LI so we have been just about everywhere in the Sound. Then once a year we try and do a long trip for a week and half out to Block then either go to Newport or some different ports in RI or eastern CT. I think it would be great if we did get a bunch of us together for a trip like this or if not a long one maybe even a weekend cruise while you are up.
If I can help out in any other way with info or suggestions on routes or ports just let me know.
Thanks and have a good one!