Hmm... a few objective points here:
- If OP keeps 40% and doesn't do work for the company, the company is highly unlikely to succeed. The company needs to be able to dish out equity to future employees and likely investors to succeed, and having 40% locked up in an entity that doesn't do anything for the company is not going to be attractive to those future participants.
- If OP keeps any equity, they should be doing it with the hope that the company succeeds, so that the equity will be worth something. Don't keep equity to spite your co-founder. It's not going to benefit you in any way if that causes the company to fail and your equity ends up being worth $0.
- If OP wants a fully cash deal, it's not realistic if the other co-founder doesn't have a ton of personal cash (most don't). Raising a round to buy out a co-founder at 40% of valuation isn't something ANY investor is going to want to do. That's almost half of an investment thrown in the trash, from their perspective, and they'd probably rather invest in a less complicated competitor.
- It sounds like the human relationship between OP and co-founder is broken and it is not worth pursuing working together, as that alone would likely lead to the failure of the company even if everything else works out.
That said, my thoughts would be:
(a) Stall for a month to get to the cliff so you have slightly more leverage.
(b) Work out a deal where you're not keeping that much equity, but you're keeping an amount such that the company is still bound for success, and that your smaller amount will actually be worth something. Owning 40% of $0 is still $0. Owning maybe 5% of $1 billion is something.