as to the use of venture capital, indeed, no investor will ever allow this -- if they have a say. seed stage funding is most often convertible debt, and the investor does not have a say (legally; but you damn well better do what they say anyway). i'm actually quite surprised that a seed investor would be noncommittal on it. however,

1/ that's the other cofounder's problem, not OPs. the way you phrase it is as if the OP is putting the other cofounder out on a limb with an unreasonable request; that is not the situation here.

2/ the other cofounder doesn't have to use capital, they can take on debt (convertible or straight debt).

It's an absolutely wonderful tradeoff if the business will be run better and more efficiently with just the one cofounder. A no-brainer really. Not doing it indicates a scam. In both cases, OP should insist on a buyout. So there's really no difficult decision here -- on OP's part anyway.

Of course with the business being "underwater" we are talking about a personal guarantee on straight debt. So again, how much does the other cofounder believe in the business and that his motives are pure?

The other cofounder can sidestep this whole thing with various shenanigans, however that doesn't mean OP should just submit. A year of OPs life is worth it to stick to his guns, even if the outcome is inevitable. It's not as if OP has to invest any effort to see through his position.