Looks like you will have to swap the transmission and rear axle out to accomplish your goal. The 1937 216 bellhousing has provisions to mount the brake and clutch pedal, but it is not friendly towards modern transmissions. Jim Carter, or Buffalo Steve have a 1948-1954 bellhousing that has beem modified to accept the pedals. These bellhousings will bolt into your chasis, and to any 216,235 or 261 engine. The advantage is that they use a modern gm bolt pattern for the transmission so you have more transmission choices.

There is plenty of information available about transmission and rear end swaps.

A quick search and you will find others have ran T5 and A833 transmissions. These are OD transmissions that work well with gears in the 3.73:1 to 4.11:1 range.

1955-1959 gm axles are also a popular swap as are the later 1960s 12 bolt truck axles.