I want to say that I have decided to switch some of my regular fast food choices to fast food choices that do not contain meat as a result of reading this post and have added frequent reminders to my phone to help me incorporate this change. I also found while considering this that if you want to encourage people to eat no meat to earn money, you have to consider the effect of them just eating less meat to save money.
For instance, I found this idea interesting, but I was concerned about possible side effects of the decision, and then started getting into what seemed like the equivalent of bizarre ethical weeds way off of the original track of the argument.
Then I tried to take things back to the original more concretely and realized I may be able to save around 11 dollars a week just by switching my current choices at Taco Bell (which do contain meat) to Bean Burritos (Which don't, and are cheaper, and are comparably tasty) and after thinking about it figured that if the first offer was even mildly tempting, an offer which is more than an order of magnitude more financially tempting and requires significantly less effort on my part is a very easy decision to make, even just ignoring the ethics altogether.
But while I started thinking about this at all because you mentioned the moral argument side, I'm pretty sure I ultimately made my decision on the money saving laziness side. Considering this perspective does make "Cutting back meat from your diet to save money." seem to be cast as a reasonable and ethically/financially tempting middle ground for someone who did not want to move all the way to vegetarianism (for whatever reason).
Ironically, while I did move closer to your stated moral goal, I'm not actually sure if my reasoning was entirely rational. But it certainly seems to be less wrong then my previous decisions at the moment and I'm certainly curious what other people think of it.
If you're somewhat motivated by moral arguments, but not prepared to go all the way, eat meat from big animals, like cows, and not small animals, like chickens. Also, if you are motivated enough, eggs are really bad.
There is an orders-of-magnitude difference between different kinds of meat, which means switching to entirely beef and dairy is almost as good as becoming a vegan. Sources: this, and this.
Also, if you are only sort-of motivated, watch some undercover factory farming videos. You should alieve in the consequences of your actions.
I notice that a large fraction of Effective Altruism people are vegetarian. This makes sense: in general Effective Altruists take moral issues seriously, even when that means changing your lifestyle. I'm not sure it's a good balance, though.
One way to think about this is to convert it into money. How much would I need to be paid to give up eating meat? All animal products? How much money would I need to spend on myself to be about as happy as I would be with less money but continuing to eat animals? I'd probably be willing to go vegetarian for about $500/year, vegan for maybe $2000/year.
It turns out you can probably pay to convince other people to be vegetarian much more cheaply than that. I estimate the cost of a vegetarian-year at $4.29 to $536 while Brian Tomasik estimates $11 with better methodology (which I looked at). This is by placing ads on facebook for a site where people can watch an animial cruelty video and ideally become vegetarian or vegan.
If you would get more than $11/year worth of enjoyment out of continuing to eat meat, why not give $11/year to convince someone else to not eat meat for you? Or give $50/year and be on the safe side?
(While you're giving money, you should probably give it to the organization that you think will do the most good with it, which I think is probably one of GiveWell's top charities. The nice thing about money as opposed to actions is that it's easy to redirect.)
I also posted this on my blog.