Get tile URL with projection different than 900913

Question

I have the following code, which should display a slippy map showing tiles producted by me with mapnik:

Proj4js.defs["EPSG:31258"] = "+proj=tmerc +lat_0=0 +lon_0=13.33333333333333 +k=1 +x_0=450000 +y_0=-5000000 +ellps=bessel +towgs84=577.326,90.129,463.919,5.137,1.474,5.297,2.4232 +units=m +no_defs";
var latLonProj = new OpenLayers.Projection("EPSG:4326");
var salzburgProj = new OpenLayers.Projection("EPSG:31258");
var bounds = new OpenLayers.Bounds(426249,294999,426251,295001);
var maxZoom = 19;
var minZoom = 11;

var map1 = new OpenLayers.Map({
               div: "map1",
               allOverlays: true,
               maxExtent: bounds,
               maxResolution: "auto",
               projection: salzburgProj,
               displayProjection: salzburgProj,
               allowSelection: true,
               units: 'm',
               controls: [new OpenLayers.Control.PanZoomBar(), new OpenLayers.Control.Navigation()]
    });

var layer1 = new OpenLayers.Layer.XYZ(
                 "layer",
                 "tiles/",
                 {
                     sphericalMercator: true,
                     crossOriginKeyword: null,
                     buffer: 1,
                     getURL: get_my_url
                 });

map1.addLayer(layer1);
var center = bounds.getCenterLonLat();
map1.setCenter(center, minZoom);

function get_my_url (bounds) {
    var z = this.map.getZoom();    
    var x = long2tile(bounds.transform(salzburgProj,latLonProj).left, z);
    var y = lat2tile(bounds.transform(salzburgProj,latLonProj).top, z);

    var path = z + "/" + x + "/" + y + ".png"; 
    var url = this.url;
    if (url instanceof Array) {
        url = this.selectUrl(path, url);
    }
    return url + path;        
}

function long2tile(lon,zoom){
    return (Math.floor((lon+180)/360*Math.pow(2,zoom)));
}

function lat2tile(lat,zoom){
return (Math.floor((1-Math.log(Math.tan(lat*Math.PI/180) + 1/Math.cos(lat*Math.PI/180))/Math.PI)/2 *Math.pow(2,zoom)));
}

I have taken get_my_url() from here (and customized it) and long2tile and lat2tile from here.

The problem is that I do not get the correct tile urls, probably because long2tile() and lat2tile() refers to projection 900913 and not to my salzburg projection 31258.

How can I modify these functions in order to get correct tile urls? Maybe can I use some tuning parameter given in 31258 definition at the top of my source?

Thanks in advance.