I will respond here although I don't want it misunderstood that I know something about gardening in zone 9 or growing carrots in containers. I don't.
Before we get any further from that May 26 statement above, I should correct something that might also be misleading. The
last time I tried "fluid seeding" with cornstarch gel was with lettuce seed. I expected it to work well because it had done a good job for me with carrot seed. If you search in TEG for cornstarch gel you will find me telling about those experiences.
What I guess that I was thinking back in May was that I was trying to better space lettuce seedlings by using the gel. It was not successful! Carrots still had to be thinned when I used it for them. And, I really think that the gel isn't worth the bother for lettuce.
Carrot seeds don't germinate quickly like lettuce. They have to be just below the soil surface because they are tiny and yet, carrot seed takes weeks to sprout. Drying out can really lower the percentage of seedlings showing up when they finally do!
Cornstarch Gel greatly improves the carrot seedling numbers.
However, carrot seed is also available pelleted. Good News! Pellets are real help in having a good stand of seedlings. However again, making and using the gel isn't at all difficult

. By the way, I would not immediately run water on the soil after putting in the gel and seed. Give them a little time to
congeal a relationship!
My biggest problem with carrots might be just the rocky soil that I have to grow them. Another problem is that DW thinks that they should be wonderfully long. They can be short and just as tasty! She is happy peeling long carrots but I don't think you even need to peel carrots. I'm willing to just scrub them to tear up that skin a little.
I think that I might grow a chantenay variety this year: Caracas. Chantenay varieties that I have had before must have been too
inelegant for DW! Caracas is listed as a baby carrot so maybe chubby cuteness will make up for length ... I can also buy the seed as pellets

.
Steve