I once looked at a Pearson 35:
It obviously has a centerboard, but it wouldn't be a boat to beach to dry out (unless you careened it).
I think your Mogan 30 is similar:
I also thought about a Tartan 37 with centerboard, but I noticed in the story of Tigger, a Tartan 37 that circumnavigated, that the owners simply glassed the centerboard up into the raised postion at one point because it caused more problems than it solved. Some have systems that fail, and others rattle quite a bit, etc.
By comparison, this is what parking an Ovni or Southerly might look like:
Hopefully, a newer boat like the Southerly or Ovni wouldn't have problems for awhile. Good luck with the Morgan-- she's a classic.
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Jim H
London, UK
Aurora, a mighty Cal 20 (Portland, OR)
Southern Rival, a seasoned Rival 34 (Gosport, UK)