Looks like I'm late to this discussion, but I will pass on a bit of what I know in hopes that it helps. I think the advice you've gotten is good, but I find some of it to also be a touch misleading, But keep in mind, what follows is all based on my experience, which is limited in ways. First, I agree that, yes, given your interests, you may want to consider an Educational Measurement program; however, with that being said, the difference between educational measurement and quant psych programs is sometimes very small (and I will stress very). Essentially, it's the focus and the questions that differ, the methods and methodological training are, in many cases, nearly the same. If you examine programs/programs of study and talk to and interact with people from both fields, you'll quickly come to realize this. I've had the pleasure of working with both, and I will be the first to say that at times the difference seems almost trivial, in my experience. I will say, though, that quant psych programs are generally more quantitatively-oriented.
As far as your mathematical background being an issue, it's going to (heavily) depend on the program to which you apply and your area of focus. But in all, I don't think it's an issue and I know of many quant psych/measurement students with little to no math background (you can pick it up along the way! And I agree with others, take such courses outside the Psych dept, if possible). I think this thread seems to slightly overemphasize mathematical training as some sort of requisite, with people even saying advanced mathematics is absolutely required for quant psych. Quant psych programs are not stats programs, and are thus much more forgiving in this regard (try getting into a PhD stats program without at least Analysis). Simply put, if they were stats programs, they'd be stats programs (except for maybe Ohio, I really can't tell the difference between that and a stats program lol). All jokes aside, they can be like stats programs, but advanced math a hard requirement? No, it simply isn't true, and I think some are forgetting or simply overlooking the fact that there is a lot of applied work being done in quant psych departments. A lot. Look in journals such as the Journal of Personality and so on and you'll see some great quant psych people from great quant psych schools doing more applied, but great, stuff. Many programs accept both types of students, those with more applied interests and those with more theoretical interests. Focusing more on the use (not creation) of analytic techniques flies in some quant psych depts. But now I will say this, the more math/theory the better lol. But many programs have a great deal of flexibility, and if your interests are more applied then that certainly shouldn't stop you. The fact you have stated an interest in a method (i.e., HLM), that's a good start right there.
Absolutely agree that programming skills are huge, and you should jump at the opportunity to learn R. Sometimes SPSS is useful, sometimes it's not. The fact is, you'll want to know multiple software packages (and languages, too, shoot, don't stop at R, pick up Python and Java, if you can). That's it for right now, if anything else comes to mind I'll be happy to give advice. I think the advice here has been good, I just wanted to add my piece.