Clay I think you will be fine with the pickering in a bigger pot, just don't saturate it with water. Mine grew quite fast when it was in a pot and even faster in ground. It only looks like a 7g anyway.. 3g -> 7g isn't really a huge upgrade in terms of pot volume, though my experiences are from a FL perspective and not CA. If you have not, I would suggest pushing the bamboo pole the pickering came with further into the pot to make sure it doesn't rock too much in the wind, since it is a larger volume.
I have had good experience with TT both in shipping a 7g Valencia Pride and a 3g cotton candy berry(I was being lazy one day and had an item shipped rather than drive the 20m to their retail nursery) and at their retail nursery in fort Myers in which I've bough a Pickering, FL Haas avocado, Glenn (died in a tropical storm unfortunately), and a Tikal Sapodilla.
Congratulations.
On a second eyeball of the pic, it looks like the pot may be 15g or larger, if that is the case I'd suggest stepping it down a size if possible.
Word of advice with potted plants and incorporating extra peat into the mix - monitor the saturation of the peat somewhat carefully. Peat can be quite hydrophobic when it becomes dried out and has trouble being re-wet unless it is saturated in a bucket or on a drop (or rain). In my experience anyway. It can create 'dry zones' in the soil which cause parts of the tree to decline. Becomes less of an issue as it breaks down over time but can be an issue in fresh mixes of the potting soil... if you used too much.. which I have definitely done in the past
