Restore plan parameters back to model using registered models and __type__

[oliwenmandiamond]

Fixes #1458

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.23%. Comparing base (7fcd2a6) to head (800392a).
⚠️ Report is 9 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1467      +/-   ##
==========================================
+ Coverage   95.19%   95.23%   +0.04%     
==========================================
  Files          43       43              
  Lines        3119     3150      +31     
==========================================
+ Hits         2969     3000      +31     
  Misses        150      150              

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