I gather from your question, you are concerned the hull may be greater than 1 1/2" near the bottom. I can assure you that on a 22' footer, the hull thickness will be no where near 1 1/2" thick, 1/4" to 1/2" will be more like it in the areas you will want to consider installing the transducer.
The traditional location for a depth sounder is just forward of the keel (the thinking being you would like to see the depth sooner than later (as in a stern-mounted transducer) as you move forward). But locations beside the forward portion of the keel will do also. I like to be able to see the depth shallow-ing out as I approach a sandy beach for hull scrub or whatever.
Based on the O'Day 222 plan (attached), your choices seem to be:
1 - forward of the porta-potti in the v-berth area
2 - aft-most section of the v-berth either side (under the pillow area).
3 - under the starboard stove
4 - under the forward section of the main salon port settee
My inclination would be #4 , under the forward section of the port salon settee, because there would be good access to drill the hole, install, cable, and the bilge section would be relatively flat there.
The v-berth locations would be hard to get to, work in, and would have a more vertical rise.
the Stove/sink area may have other galley related storage (pots and pans? ) you would rather keep.
I am surprised you did not ask what to bed the transducer with, which will introduce a topic discussion much like politics, or religion !
I have boated 40 years, and installed a bunch of depth/speed transducers.
I have always used LifeCaulk, and been very happy with it, decade after decade. It is leak-proof, permanent, flexible, paint-able, and yet can be removed with some coaxing years down the road.
I personally would NEVER use 5200. Somebody, 20 years from now may want to remove that transducer to replace with a new one, and 5200 will not give up its tenacious grip without a serious fight, including possible de-lamination of the fiberglass. The only place I would use 5200 is somewhere where one would never-EVER want to undo the joint, such as the hull to deck joint at OEM manufacture time. And possibly the keel to stub joint, but even there, someone is going to want to drop the keel at some point down the road. I would have to do some research there, maybe 4200.
Now sit back and watch the comments fly on this one !
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Best regards.
Andre