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Great idea! However it seems that QGIS could only use the projections defined in PROJ library and LTS releases seem to be compiled with PROJ 4.9.3. It should be investigated that how much interesting projections are defined there. Equal Earth Projection is supported by PROJ >= 5.2.0 (usage in QGIS) but QGIS has to be compiled with the support.
Some of the projections are added in v0.6.0. Unfortunately chancing the origin causes rendering artifacts in countries and halo. This has to be investigated more.
Would be a very nice feature to have other custom projections available in the plugin besides the globe, such as Lee confomal or Waterman butterfly.
These have been requested before to QGIS but not available currently.
From UI perspective, choosing the projection could be an option in the dialog.
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