This is really an interesting thread, it is one of those questions that seems so obvious yet no one thought to ask it....and after searching around I could find no reference to it, which is pretty wild given all the rail information out there. I actually asked this question a couple of places on the net I go to where there are knowledgeable train people, and they all scratched their heads, but to a person they said car float was the most likely method, obviously pre the bridge/tunnels being built, but likely even post then. To a person they all said that car floats could carry pretty big loads as @S.Islander showed with his posted picture and they said logistically that was the easiest and cheapest way to transport them in the post connection era, the cost of transporting them via the poughkeepsie bridge link over the New Haven and the bother, or trying to get them through the tunnels, wouldn't be worth it in their opinion, car floats were existing service over their own tracks.
To a person they were amazed that they had never run across this question before or that there wasn't anything out there about it. They also pointed out that engines in the early days of the LIRR were likely relatively light compared to later engines, but it still was something of a feat to be able to float them at the time. I don't know for sure, but I think I remember reading some of the early engines the LIRR had came from England, wonder if they shipped them directly from there to Long Island?
