Pushing tx to the network via AJAX, without installing bitcoin
Looks like the premise of this question was wrong. Blockchain.info DOES support raw transactions via ajax however you have to include ?cors=true to the end.

Note they also require application/x-www-form-urlencoded data. Here's what my request looked like in angular

$http({
    method: 'POST'
    ,url: 'https://blockchain.info/pushtx?cors=true'
    ,data: $.param({tx:txHex})
    ,headers:{
        "Content-Type":"application/x-www-form-urlencoded"
    }
})