I've had several Allspice trees/shrubs outside here and never had any damage from frost/freezing. They have certainly been hardy down to 26 degrees with adequate soil/air moisture.
Unfortunately I live near the Canadian boarder in a ski area, it's prone to severe cold snaps of 5-10 degrees and sometimes in the negatives with the average being in the 20's. I tried growing some types of citrus that claimed to tolerate down to the 20's or high 10's. They died when temps sustained 30 F and below for a prolonged period with a all time seasonal low of 16.
The conditions during the warm months are almost tropical with typical seasonal highs of 80 plus in the day and sometimes 60+ at night with rainy trends. The warm months are too short to attempt bananas outdoors, I just rescued my outdoor blue java banana plant that was really happy out there with a big rootball, some early frost that dropped the night time temps down to 28 had ruined all the growth it had achieved starting in late spring. It's base is almost too large to repot.
I tried starfruit too, despite being grown indoors the indoor temp and my ineptitude proved too stressful for it, so it died a few months after I got it.
I have a carnivorous plant starter pot on a whim, and also because of the issue of these pots attracting flying pests. It's a cape sundew.