... and that will also be just a little too far from the wall, just like the existing one is?
Then you will need to pay more attention to the toilet schematics - you'll want to get the toilet that shows the least amount of room between the tank and the back of the wall. Secondly, you will want to measure the bowl holes centre to centre (the bolts being as close to the centre of the bowl as possible - that's why the holes are elongated) and then tighten down the flange bolts in as far back a position as possible while still having the just measured bowl hole distance. That should set it back a little more (figure about 1/4"). A squared back toilet tank lid is probably best to minimize the spacious look, say versus the Drake oval-ish tank lid.
My hallway bathroom toilet is 13" from the wall, too, and I have a good 2.5" of space showing. The Drake tank has a lip on the back, so it stands out a little under 2.5". My master bedroom bathroom toilet is on 12" centres and it stands out 1.125" from the wall. That is
exactly what the Drake schematics show as the distance to the wall. (Obviously I did not do what I just described should be done. And which I afterwards wish I had one.)
The Transitional Drake schematic shows 0.75" away from the wall. The Drake II 1.28gpf is 13/16", or 0.8125". The Entrada, 0.75". If your toilet is an other-than-Toto you will want to see what the schematics say the distance should be.
After you tighten the flange bolts down lightly, you will want to position the bowl down onto the bolts and see where in the elongated holes the bolts are - the closer to the right (left side) and left (right side) the better. Since the flange bolts are just
lightly tightened you should be able to slowly move back the bowl and hopefully the flange bolts will move back. (It's better to just measure with a ruler, no?, least the bolts angle backwards - which is why you will want a real metal nut doing the tightening instead of plastic retainer.) Hopefully. Only after you have physically measured should you tighten the flange bolts a little more and then affix the wax ring seal.