Well isn't that the only true reason?
Would you still be against Homosexuality if it was Hallal?
If not, every other reason you give would be a lie.
And lying isn't dawa. Lying is lying.
You know when people say stuff like "You shouldn't do that disgusting stuff, if you do you will die of aids", I think that makes us look worse than if we would have just said "Islam and every other reason that mentions it forbids it".
You are more likely to convince the God believers amongst them with that sort of honesty.
You may ask, what of the Non-God-believers?
Well if they don't even believe in Allah, what difference does it make who they have sex with?
If you convince one of them to be straight but not to Believe in Allah would it make any difference to his final destination after he dies?
What Muslims need to understand is who to talk to about aqeeda and who to talk to about Fiqh.
You talk to Muslims about why they should follow the rules of Islam.
If there was a Muslim who liked having sex with men, you will benefit him by convincing him not to.
That is dawa.
If there was a non Muslim that liked having sex with men. It would make no difference to him if you convince him not to using the health benefits of being straight.
Instead you would benefit him in convincing him that Islam is the truth.
And after that you can explain to him that it is harram for him to have sex with men.
This same argument applies to any issue. No point in convincing Kaffir of the health benefits of praying, fasting wearing hijab or not eating pork. If they did all that without believing in Allah it would make no difference to them.
So when they ask you about Islamic rules you follow. Tell them you follow it because Allah tells you to. And if they need more explain to them why you believe in Allah and why you believe the Quran is the word of Allah.
And if you can't explain to some that Allah exists and the Quran is the word of Allah, it is about time you learnt all that for yourself.