I've never seen a maze like this turned into a game before. Love the idea!
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Spoiler
Interesting puzzle.
Starting out by looking at the portals, Ω1 is needed to unlock ¿9, Ω2 for Ÿ6, Ω4 for Ÿ9 and ¿13, Ω5 for ¿7, Ÿ8, ¿8, and Ω7, and Ω7 for the end, while Ω3 and Ω6 do nothing.
Because of one-way paths and death markers, □3 and Ÿ7 are not accessible on a valid path. Because Ÿ9 (Mole-Rat) effectively serves as a one-way path (with the alternative Ω6 leading to the start, inaccessible due to the Troll), Ω4 is also effectively useless and ¿13 (Ladder) is inaccessible.
A starting route should pass Ÿ1 (Fish), retrieve ¿3 (Crown) and ¿12 (Key) from Ÿ3 (Delivery Boy), and use the Key on □4 to proceed past Ÿ2 (Bridge Troll). As returning past the Bridge Troll is effectively a one-way path, ¿4 (Lightbowl) and ¿9 (Earth Nugget) via Ω1 are inaccessible on a valid path.
At this point (and before further teleports), there is direct access to Ω5, ¿2, Ÿ5, □2 (flavor text), ¿10, Ω2, □5 (flavor text), Ÿ4, and Ω4. Counting Ω2, Ω4, and Ω5, there is also access to Ÿ6, ¿7, Ÿ8, ¿8, and Ω7 (and by extension, the end).
Before accounting for further creatures, the inventory has ¿2 (Paradox), ¿3 (Crown), ¿7 (Fire Nugget), ¿8 (Water Nugget), ¿10 (Wind Nugget), and ¿12 (Key). In terms of further creatures, there is access to Ÿ4, Ÿ5, Ÿ7, and Ÿ8.
Ÿ4 (High Priestess) gives ¿1 (Fishbowl), while Ÿ8 (Crazy One) gives ¿11 (Taser), bringing the inventory item count to 8 items. If the Crown is left behind, one could get ¿5 (Cigarette) from Ÿ6 (Emperor) and exchange it for ¿6 (Egg) from Ÿ5 (Mute Boy and Chicken), but the item count would still be 8.
With 8 items (Fishbowl, Paradox, Crown or Cigarette or Egg, Fire Nugget, Water Nugget, Wind Nugget, Taser, and Key), one should be able to leave the maze via Ω7 optimally.
Spoiler
There's a solution with more items. You're close though.
Spoiler
Reading it over a bit better now, I guess if one doesn't get the Crown, gets the cigarette, and uses the cigarette to get access to the ladder, the need to go past the troll is effectively bypassed.
One could then trade the fishbowl for the lightbowl, get the earth nugget, and bypass the need to visit the troll via Ω3 instead (using the taser), bringing the end item count to 9.