can I save a video transition preset that I've customized

Click on something then right-click/copy, or of course Ctrl-C for copy, Ctrl-V for paste after selecting that which you want to paste onto.

There are a number of things you can do in Premiere that involve creating complex clip/synthetic clip stacks with effects applied. If you have 'template' project files to house them, you can drag/drop and replace the media pretty easily, much faster than re-creating the blame thing each time. So for many editors, building up a store-house of things you've built is a major process for getting both faster and more accurate.

Neil

Unless I'm missing something (which is always possible if not likely) your way doesn't seem any better than the copy/paste solution that I discovered, both require a "template" sequence to store the customized transitions.  And yeah, I have customized them.  What's interesting is my solution seems to be an accident in programming (or minimally not completely thought out), cause when you control click on the transition you wish to copy, there's no option to copy and when you control click on the transition you wish to paste to, there's no option to paste...  When I was trying to figure out a way to accomplish this, it didn't initally occur to me try the copy and paste because the options were not available in the contextual menu.  Of course I'm not a programmer and may be missing the constraints that prevent this from happening.

As you've noted, there are a number of the included transistions that can't be modified then saved as presets. Of course, if you're just using them with the standard settings, you can quickly right-click on a preset in the Effects panel, Set as Default. The using the keyboard shorts for applying default transition it's very quick to apply to one or more selected clips.

To modify other transitions and save, you need to save a short sequence where they're applied and set as you wish say on a pair of synthetic media clips (project panel, new item menu, color bars, Adjustment layer, black or transparent video). It's handy to have a project with say your transitions applied to several sequences of clips this way, and drag/drop them from that sequence to the timeline you're working on.

The new Productions feature actually makes this very easy to do. Have a subfolder for transitions, within it create a project file with several sequences of synthetic clips with different transitions applied and modified to taste. Then just open that project file, drag the transition to your current working sequence.

Neil