Question on splitting neutral and ground

Background: I moved, previous house had a 4wire dryer outlet, new house has 3 wire. I have 240v system, I don't have anything inside the control box powered via 120v. I'm using a 10/4 30a power cable with an inline GFCI (same one Kal has on the electric brewery).

Please tell me if my logic/steps are correct:

-I'm going to check behind the 3wire outlet to see if there's a ground wire run. If so, i'll simply install a 4 prong outlet, swap the dryer's cord to 4 wire and be done.

-Assuming there isn't a ground wire hiding back there, I need to check if the neutral and ground are bonded in the panel correct?

-Assuming the neutral and the ground are bonded in the panel, I can split the neutral into two wires, one feeding the ground wire on my cable directly, and one feeding the neutral which runs through the GFCI.

-Can I make a small junction box (smaller than a spa panel) to break out the neutral into two wires, and everything will work?

Ok, there's no ground wire hiding, so I definitely have to explore splitting the neutral

So the question being, assuming my neutral and ground are bonded in the main panel, would this drawing work? Remember my 10/4 power cord that powers my control box has an inline GFCI. The box around the outlet is a junction box of some sort. The Neutral wire will be dead-ended once inside the control box (nothing will be connected to it)

What you are saying would work, but its a bad idea. Being as you don't have any neutral loads in your system besides your gfci. It doesnt make a ton of sense to get greasy on your electrical system just to try and make a safety mechanism work properly. If I were you I would toss the inline gfci and install a gfci breaker in your panel. tie the gfci breaker neutral to the neutral bar in the panel and the ground going to the control to the ground bar. you could sell the gfci cord to someone for the price of a gfci breaker.

Not too greasy, just need a 10/3 dryer cord, handy box and a 4 prong outlet. I'd love to keep my current setup as is, so making this little adapter, if it works, is ideal for me. I left out that I rent this house. That's a biggie.

Thanks for the confirmation it will work, even if its not up to code