I (British citizen) have an American partner so I feel your struggle as keeping him here has been a nightmare! Part of the reason I started looking into this career in the first place is because I was doing enough of the legal research with none of the reward, haha.Fair enough, thankfully in a situation where my partner fulfils all the criteria. nonetheless indeed it is a risk for them too.
Anyway, just commenting to say that if your partner qualifies as a sponsor, I wonder why you haven't started that process yet? It's harder if you aren't married but still doable if you have been together long enough. I feel like that would help your application, but of course I don't know anything about you / your situation, and I am not qualified to say anything for certain! But surely worth a try.
Either way, I would tick the 'eligible' box and explain you have a partner who is a British citizen willing and able to sponsor you. I do think that would help! No harm in trying, as it isn't untrue!
Best of luck