I had similar issues for my project, as the IAT for anti-Muslim prejudice which is most often used is based on Arab identity. The conflation between the "Arab" and "Muslim" identity is a prevalent issue in this area. I didn't find any other implicit measures. However, I used Behavioral Intentions Toward Outgroups (Esses & Dovidio, 2002) and modified it for Muslims to measure individuals' social distance with Muslims. Additionally, you can measure individuals' Intergroup Anxiety (Britt et al., 1999), which is a strong mediator of prejudice as well as their endorsement of policies that are anti-Muslim. These are the ways that I was best able to address the issue you initially touched upon. 

I think the only other measures I've seen are more behavioral, like how close you are willing to sit to a person from another group, whether you hire someone with a certain name on their resume, or how you respond to emails (with the person's picture/name shown). The IAT is suboptimal for various reasons you probably already know. But it does tend to be related to similar things, like biases in the shooter task (see attached link).

http://psych.colorado.edu/~jclab/FPST.html

The Go/No Go test is a reaction-time based method that can be applied to assessing implicit prejudice but does not have the limitation of being a 2-category comparison that the IAT has. Nosek, B. A., & Banaji, M. R. (2001). The go/no-go association task. Social cognition, 19(6), 625-666.