How to merge Japanese characters into Roman letters (or the reverse) -- looking for advice

I copied your とうふ text from your post, added tofu to another text layer with the Hiragino Kaku Gothic Pro font I had on my system, created a simple opacity transition between the layers, created an adjustment layer with animated Directional Blur, Gaussian Blur, Simple Choker, and added and adjusted Bevil Alpha to get this:

If you convert the text layers to shape layers and animate the position of a couple of the extraneous parts of the Japanese characters you could eliminate the disappearing bits, but this looks pretty good to me.  Here's my project file. It was fun.

Not really a good way to go abhout this, given how the languages and glyphs are constructed to begin with. Rick has explained his go-to technique already and I would just add that if you can, simply avoid such complex morphs. They simply tend to look extremely weird and it's usually much more efficient and more visually pleasing to have "invisible transitions" like dispersing letters into particles and reassembling them, using a blur whip/ cross fade while they move and similar.

Mylenium

Trying to morph one font into another isn't going to be easy if you stick to After Effects. You can play with displacement maps, liquify, mesh wrap, and other tools but the fonts can be very complex, especially if you are going from Japanese Characters to Roman (Latin) characters. Asian characters don't really have serifs so I would stick with Roman fonts that had a similar look.

I would open up Illustrator, add your Japanese characters, add your Roman Characters, convert both of these layers to outlines, then line up one shape with another and enable the blend mode to merge them. Play with the paths and settings until you get a few shapes merging. Start with the fonts, convert to outlines, select colors, set up blends, release to layers, save, import as a comp cropped layers, open the comp, set all layers to be one frame long with some room at the front of the comp, group layers by color, sequence layers and adjust timing. Here's a sequence of screenshots.

Add Text

Convert to outlines and color

Set Up Blend:

Align and release to layers:

Import as a comp:

Organize layers and set up for sequence:

Sequence layers:

End up with this:

Here's a quick tutorial that I did a long time ago. It shows the steps to go through. I've been using this workflow for almost 20 years. It's still the easiest way to morph shapes with predictable results. When you have the comp set up the way you want it, embed the comp in another comp (or Pre-compose everything) and apply time remapping to adjust the timing of the morph. I usually pick between 30 and 60 steps so that my default transition between shapes takes 1 to 2 seconds in a normal comp.