The last year that Ford produced a factory top shift three speed for the flathead was 1939, and this is the preferred one by hot rodders. They had synchronizers on second and third, just not first (the assumption being you only shifted into first when stopped) from at least 1935 and up, perhaps 1932, memory's a little fuzzy on that. The reason folks center on the 1939 version is that it had improved shift fork strenghth over the earlier versions, though they weren't terribly weak. A popular upgrade is to use a gear set from the Lincoln Zephyr (sometimes called 25 tooth, they "drop right in") because of their gear ratio being more favorable to acceleration. These gears are being reproduced by Speedway Motors, www.speedwaymotors.com.

If you use a bellhousing from a '49-51 Mercury you can bolt on later model Borg Warner three speeds which came in Fords, Jeeps, and others. It has a top cover access design, and handily the '39 top cover with shifter bolts right on. Versions of this trans built from the mid '60's will also have a synchro first.

Just to mention another alternative, Cornhusker Rod & Custom makes an adapter to put a T-5 trans that's very popular today. You get overdrive 5 speed, and floor shifter. Read the link, http://www.cornhuskerrodandcustom.net/ytrans.htm
You do have to convert from the torque tube drive also.