Work on lower body “attitude”
I went from 26" to 22" beam after a year. The 22" boat felt much, much better to me (plenty stable, not so wallowy/bargey), but we are talking about different boats and different people. I am short (5'2"), which in itself helps stability.
It probably would help to focus first on both psychological factors and on lower/middle body attitude.
If you have not taken any paddling lessons, that will probably help. At the very least, they will teach you how to deal with wet exits and re-entries. Once you have learned those, the psychological bugaboos associated with tipping will be less boisterous.
Also, do you know how to swim? My impression is that the people who are most fearful of tipping turn out to be those who do not know how to swim. If you are uptight, you are more likely to transmit that tenseness to the boat; it's not only a matter of whether the hull is tippy but how you respond to its feel.
An exercise that I enjoy--it makes me feel like the boat is an extension of myself--is to sit in it in shallow water and hand-paddle it: forward stroke, backward stroke, turning including leaned turns substituting hand for paddle blade. Of course, the hand/arm does not give as much oomph as a paddle, but it does more than you might think, especially combined with a lean. For the forward stroke and reverse stroke, I use both sides at once for obvious reasons. I find this exercise analagous to x-c skiing without poles (on flat ground). It focuses your attention on your lower body and its tremendous effect on what happens. Once you have the lower/middle body relaxed and ready, add in the arms and paddle/ski pole.