First time in cruising, in mexico, on a 20'''' sloop.
John Letcher sailed from California over to Hawaii and then back to the Pacific Coast (the Northwest, as I recall) on his little 20'' bilge keeled ALEUTKA (sp?). John Guzzwell sailed around the world on his little 20'' Laurent Giles designed sloop, TREKKA. But both those boats were very well found, properly equipped for the cruising grounds they visited and, most importantly, both single-handed sailors were eager for that kind of challenge. The suitability of your plan - which is not unusual by any means, but usually not in so small a boat - is most dependent on your own skills and motivation, not just boat issues (as you acknowledge).
Rather than detailing where your boat may not be suitably equipped at the moment (e.g. your ground tackle is too short and probably not beefy enough), let''s look at the 3 main challenges you''ll face: 1) the possibility of an offshore blow in the 30-40 kt range e.g. near Cedros Is. when going down, with sea and air temps much like you see in the Channel Islands (Brrrr!); 2) some surgy anchorages, which can detract from comfort aboard (enjoy seeing the sights ashore!); and 3) a long windward bash getting back up to San Diego (windward work for an extended period, which your boat apparently does not do well in, and which you can''t compensate for by motoring). You need to feel comfortable with all 3 of these challenges to enjoy yourself, I would think.
Two suggestions: First, Latitude 38 covers this kind of issue all the time, since it''s a common question for California sailors who want to enjoy MananaLand for a spell. In fact, L38 sponsors an annual Baja Haha that leaves San Diego each October. (That''s a good answer to your timing question for going down, but coming back in December is not recommended; spring is better). L38 does not accept boats your size in their ''rally'' (minimum is 30'') due to safety concerns and they''re quite prudent & knowledgeable, so that''s a hint. Start reading L38 routinely (free at WM stores if you find out when it normally arrives; they disappear fast) and review some back issues on-line to read past Letters that will talk about this (www.latitude38.com). Over time, you''ll gain much insight into what you''re thinking of doing.
Second, set up a cruise that''s more representative of what you have in mind, see if you enjoy the cruise and your boat can handle the conditions, and then reflect on what additions/changes you & your boat need to consider. Hopping e.g. over to Catalina, perhaps then visiting Santa Barbara Is. and then returning to SoCal is not a good test. Instead, consider sailing up to the back side of Santa Rosa (if you''re coming from the LA/San Pedro area) that will require sustained windward work and will be a long hike, like a ''first installment'' of getting back from Turtle Bay or Cabo). Then anchorage hop down either side of Santa Cruz (open roadstead anchorages but with varying amounts of protection from surge). From a suitable point on Santa Cruz, put in a long run back that will again give you 24+ hours in the Channel, so you can feel the afternoon winds & seas, and also the all-night sea/air temps. Try to take your friend with you; great way to test his/her commitment and your compatability.
Good luck to you. There''s a lot of adventure wrapped up in your plan, and not much expense even with some boat mods. But it''s also a serious cruise plan, both going down and coming back.