Ok, that's great news about not using the ether. Bad, bad ju-ju! So, we are probably ok there.
When you say you cleaned the entire choke assembly, please explain. Your carb should have a two piece, knob/cable/housing and a "valve set" attached to it that screws in to the carb with plastic threads. See items 12 and 20 in the link below.
http://www.boats.net/parts/search/H.../BF9.9DK0 LHA /CARBURETOR (MANUAL)/parts.html
The cable must be attached to the valve set prior to installation and this makes the two pieces come off and go back on the carb as one piece.The metal "plug" that is attached to the end of the cable is the choke "mechanism". It simply blocks or unblocks the enrichment passage when the cable is pushed or pulled. Did you remove this contraption from the carb and spray clean the passage and cross drillings underneath?
I have seen the plastic threads for these strip badly and cause the choke not to work correctly. It is also possible for the little "plug" to come off of the end of the cable and then there would be no choke. And, the cable housing breaks right where the permanent bend is just above the plastic threads. This can cause the cable to flex too much to unplug the enrichment passage and, again, no choke action. This also lets dirt enter the cable housing and valve set and will, eventually, find it's way into the carburetor.
If you bought the outboard new, then you would know whether or not the valves have ever been adjusted. If they have not, then now is the time to get that done. They may be a bit tight and be the cause of this problem. Valves tend to wear and go out of adjustment in the first 100 hours of the engine's life. They do wear after that of course but the initial break in wear can be dramatic. So get them adjusted if you haven't already.
As far as your compression seeming "ok", that's all well and good but not very scientific.The ONLY way to determine if the compression is adequate for cold start is to do a compression check using a compression gauge and proper procedure. It is not hard to do and compression gauges don't cost a great deal. However, it IS hard to find the right adapter for these spark plug holes. I made my own but you might have some trouble there. Autozone has a tool lending program wherein you might be able to obtain what you need for a returnable deposit if you choose to do the work yourself. Adjust your valves prior to doing this test so that you get accurate results.
Those are the things I would check and correct initially for this complaint. Good luck and don't hesitate to ask any questions.