Experimented a lot with tile styles, committing the most promising one. Still need to figure out the best tile size though.

game/test_iso_tileset/new_tileset.tres

@@ -0,0 +1,47 @@
+[gd_resource type="TileSet" load_steps=2 format=2]
+
+[ext_resource path="res://test_iso_tileset/test_tiles.png" type="Texture" id=1]
+
+[resource]
+0/name = "t3"
+0/texture = ExtResource( 1 )
+0/tex_offset = Vector2( 0, 0 )
+0/modulate = Color( 1, 1, 1, 1 )
+0/region = Rect2( 106, 15, 52, 27 )
+0/tile_mode = 0
+0/occluder_offset = Vector2( 0, 0 )
+0/navigation_offset = Vector2( 0, 0 )
+0/shape_offset = Vector2( 0, 0 )
+0/shape_transform = Transform2D( 1, 0, 0, 1, 0, 0 )
+0/shape_one_way = false
+0/shape_one_way_margin = 0.0
+0/shapes = [  ]
+0/z_index = 0
+1/name = "t2"
+1/texture = ExtResource( 1 )
+1/tex_offset = Vector2( 0, 0 )
+1/modulate = Color( 1, 1, 1, 1 )
+1/region = Rect2( 47, 8, 44, 23 )
+1/tile_mode = 0
+1/occluder_offset = Vector2( 0, 0 )
+1/navigation_offset = Vector2( 0, 0 )
+1/shape_offset = Vector2( 0, 0 )
+1/shape_transform = Transform2D( 1, 0, 0, 1, 0, 0 )
+1/shape_one_way = false
+1/shape_one_way_margin = 0.0
+1/shapes = [  ]
+1/z_index = 0
+2/name = "t1"
+2/texture = ExtResource( 1 )
+2/tex_offset = Vector2( 0, 0 )
+2/modulate = Color( 1, 1, 1, 1 )
+2/region = Rect2( 1, 2, 32, 17 )
+2/tile_mode = 0
+2/occluder_offset = Vector2( 0, 0 )
+2/navigation_offset = Vector2( 0, 0 )
+2/shape_offset = Vector2( 0, 0 )
+2/shape_transform = Transform2D( 1, 0, 0, 1, 0, 0 )
+2/shape_one_way = false
+2/shape_one_way_margin = 0.0
+2/shapes = [  ]
+2/z_index = 0

game/test_iso_tileset/test_tiles.png.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="StreamTexture"
+path="res://.import/test_tiles.png-5a88da34746bccf98b2c562f5067716b.stex"
+metadata={
+"vram_texture": false
+}
+
+[deps]
+
+source_file="res://test_iso_tileset/test_tiles.png"
+dest_files=[ "res://.import/test_tiles.png-5a88da34746bccf98b2c562f5067716b.stex" ]
+
+[params]
+
+compress/mode=0
+compress/lossy_quality=0.7
+compress/hdr_mode=0
+compress/bptc_ldr=0
+compress/normal_map=0
+flags/repeat=1
+flags/filter=false
+flags/mipmaps=false
+flags/anisotropic=false
+flags/srgb=2
+process/fix_alpha_border=false
+process/premult_alpha=false
+process/HDR_as_SRGB=false
+process/invert_color=false
+stream=false
+size_limit=0
+detect_3d=false
+svg/scale=1.0