Yes, this is a weird problem unfortunately. Even the East Coast Greenway takes a seemingly completely unnecessary bump north in Eastern CT. If I had to guess it's because there aren't many safe for bikes ways to cross both the Thames and Connecticut Rivers. I found it very difficult to plan a route when I was trying to do a coastal trip from Providence to NYC.

FTR the Greenway itself goes south from Pomfret to Moosup then East across Sterling into Coventry and picks up the Cranston/Washington Secondary path, your Option 3. It is well marked due to being part of the Greenway, if that helps.

For your actual question - on option 1 44 is actually fine other than a couple spots if you are a confident cyclist. You might feel better deferring a little south to 101 then pick your way to avoid Rt. 6. Either way your problem is going to be anything inside of 295, which will be pretty dense with traffic on any decent through roads.

I might check the Narragansett Bay Wheelmen's maps page for rides as they usually pick good roads. If you contact them they might help you out as well.