The Model 1 was the only option from F-W available at that time for side-mounting. The Model 2/3 are the same thing with either both floor-mounted hardware or one floor and one side-mounted. The distance between sets of holes isn't relevant - with small changes it's the same product for approx. 20 years. If the car were older - or perhaps someone used "leftovers," it's possible the Washington Mortuary equivalent could've been used - the bracket/bar are slightly different based on generation. A final and less common option is Baumgardner - which was still producing product up to at least 1964.
The low-headroom cots at that time were the Model 21L (single-level, "two-man"), Model 54L (two-level, "two-man"), Model 32 (Multi-level X-frame, "two-man") and Model 27 (Two-level, "One-Man"). Of course, folks didn't always follow the "book" and could've used the regular height cot equivalents despite having a low-headroom vehicle. I think for 1966 with side-mount hardware obviously having been present - the most likely would've been a Model 32.
Congrats on your purchase. As far as I am aware, you have the second Chrysler-branded ambulance from the time period that survives today.