It's a sticky situation to be in. However, since you're not an employee and a Co-Founder; would suggest you go ahead & give it a try to work things out. Essentially, if you're partners you would already be having different work areas. (Tech/ Business/ Finances etc) both of you wouldn't be doing the same things (in case you are bifurcate it & then you won't be having either of you in each other's territory).
What are your plans if you do move out? Is it another business or join a firm or taking some time off? If it's another role or a business then you could ask to stay on board as an advisor. If not then try the talk to move out. It would be fair for your partner to know you're thinking of this & both of you need to know why this is happening-you could also be at fault.
Also, since you're planning on leaving even your present partner has a right to the original equity-you could sell it back to him. It's important he's aware of this before you start speaking to other potential buyers. No matter how strained a relationship is, it doesn't entitle you to use any backhanded tactic or lose the integrity and ethics you started with. Some business partnerships work some don't, & really which partnership is a smooth sailing? It's always with a few ups and downs that test the tide of time.
Good luck to both of you.
This question should be answered in the details of the grant of equity you received. Unfortunately not every company thinks to include the terms of an exit in their equity deals, and that can cause legal problems. "Best way" doesn't describe what you hope to get from the sale of your equity stake or to whom you intend to sell it, if you're even allowed to.
First thing to do is to read the details of your granted shares to see how you've already agreed to proceed with any potential sale. If undefined, then first have a non-confrontational conversation with the other stakeholders to see if you can come to a friendly agreement. Lastly, hire an attorney. You're going to need one regardless of to whom you sell your stake or how friendly you are with the other stakeholders.