Welcome to the cold natured Merc triple looper. I had the 2002 edition and that was almost verbatim my problems. What control box do you have....Commander 2000 or 3000. The 3000 has the big black button on the base of the handle used for fast idle? Why am I curious? I personally prefer the 2000 with the lift lever mentioned below as it is much easier to engage the choke function.
The bulb should pump up firm when the carbs get full. I had to replace my fuel line at 10 years due to the inside scaling, a tan scale shaped in little semicircles, the diameter of the inside of the line....3/8". I replaced the bulb with the OEM while I was at it.
Just save some time here. get a new fuel line and Merc/jQuicksilver squeeze bulb. Ensure that the arrow points toward the engine when installing. Check all the fuel lines for crud while you have the thing open. Very possibly your extent of cold natured problems can be attributed to lack of fuel prime in the carbs.
Second, you need to ensure that you use the fast idle and have it at max. On the 3000 you have to put the shifter in N and wiggle it while pushing the button till it engages (pushes in about 3/8"). Then advance the throttle/shift handle to WOT position while holding it in. What you just did in doing that was to disengage the shifter mechanism from the handle and it functions as a throttle only. On the 2000 there is a lever at the rear of the control that you lift up. Lift it as far as it wants to go.....roughly 80 degrees up from where it is when you are through using it. On the 3000 bringing the lever back to N will reset the lever to function as throttle and shift. On the 2000 just push the lever down onto the box when finished, before you shift into F......saves the gear train. Little additional info, the idle is 675 +/- 50 rpm per the service manual. If you are too low it will want to die when you shift into gear and too fast you crunch your gears when doing the same movement.
The key switch has a detent and that's your fuel enrichment, aka choke. I used to push mine in for 15 or so seconds and roll the key on over to start while keeping the key pushed in. If it doesn't light off in about 15 -20 seconds, re do the bulb and start over with the enrichment. Be ready as soon as it lights off to cut the rpms back to 1500 give or take. If it wants to quit on you leave the throttle where you had it, just push in on the key till it recovers and let go....key will be in the ON position during this additional priming with the engine sputtering/running. Give it a minute or so to warm up and you are good to go.
On the first hole shot of the day, hands down the sucker would fail. I'd have to nurse it up onto plane and run it like that for 30 seconds or so. Then I could cut the throttle back to idle, get back in the hole, fire wall it, and she'd take it like a champ. Like yours, usually started immediately the rest of the day with no choking or bulb squeezing and take the hole shot every time unless I shut it down for like an hour or so. Then a little fast idle usually did the trick without having to prime again.
This was a dream of an engine and would run my little boat right at 50 gps with just me. I loved it........once you get it going in the morning...a PIA!