FYI, the adapter plate with work to fairly easily adapt an EJ engine to an EA transmission. It will not work the other way around. It could be done, but it would require a custom flywheel to take up the extra depth.
The 6MT is roughly the same size as the 4EAT transmission. In '87.5, the EA82 transmission tunnel got bigger to accommodate that. It will easily fit in the newer EA82s, it's been done in the early EA82s, but at the very least requires a spacer to lower the transmission in the tunnel (but that's not ideal for driveline angles).
It's been done in EA81s, but AFAIK only with tunnel modification.
Anything is possible with enough money and fabrication. But far from bolt-on. Also absolutely zero reason for it unless you've done the engine swap (no '80s engine can produce enough power to require the strength), and other driveline modifications.