What I'd suggest is using a circular saw and clamping a guide to the board. And if you don't need the full 10' for your railing then cutting it to the rough length will help.
Instead of needing to move the heavy piece through stationary equipment this makes the piece stationary. You probably would need to get a little creative to find a straight-edge that's long enough, and if you take your time setting it up you can use a couple pieces. You can finish the cut by flipping it and repeating it on the other side--or using a handsaw following the kerf of the circular saw.
You could always use your stationary tools--a bandsaw will work well, as long as you have 10' both in front and behind the saw and appropriate infeed/outfeed support (and/or a second person).
A tablesaw would also work, but as you noted a 10" tablesaw won't be able to cut all the way through. Typically they have a max cutting depth of about 3 inches--and that's a lot to do in a single pass, especially with a full-kerf blade. You'd likely want to cut about 1" deep, raise the blade another inch, and do another pass, flip it, and repeat (or use a handsaw to cut the last inch or so). If the board is isn't straight and true you won't get a perfect cut this way, but if you leave extra you can clean it up.