visual - Nodes & Tunnels

^{An entry in Fortnightly Topic Challenge #33: Surface Geometry Mazes}

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Behold, a tricky maze created on the surface of a cube. There are 'nodes' to collect and tunnels to traverse, are you up to the challenge?

I have unfolded the cube and created a legend to aid your mission, you can also find the rules below! (Click images for a closer look):

Here is the maze in all it's unfolded glory, remember even in this condition it is still a cube!:

Answers should adhere to the above parameters, shown preferably with a nice long scrawl over my original image but feel free to improvise!

There is at least one correct path but as with the nature of such a puzzle other solutions may exist. The first answer given that meets the criteria will be awarded the tick, if it's quite different to my solution I will also share mine as a second answer :)

Extra information for those that like to think out of the box, you can't jump walls, climb, fly, reach that node just over there, squeeze past your old paths, re-use tunnels or become a giant to take the whole maze and all it's nodes in one grab, etc ;)

EDIT: Quick rules clarification as a relative brought it up when attempting the puzzles, use of tunnels is optional. Whether completion is possible without them is another thing!

Good luck and I hope you have fun solving it!

Answer

This seems to work:

Green is the path. Purple is showing how many times we enter each face.

Highly sophisticated method of solution: Trial and error. (I started by filling in things that were forced, then just drew stuff. I ended up with a couple of loops and some bits that wouldn't connect, and fixed things up incrementally.)