There are a variety of models solving accuracy and RT that have been pretty well tested and LBA is probably fine (I haven't used it). If you don't want to go that far there is a rather simple way to analyze data controlling for SAT that has much better mathematical properties than IE scores (which, as Mike said were named by me, but offhandedly proposed by Townsend & Asby, easily conceptualized as related to older rate of information scores holding information constant, and probably popularized most by Shore).
The first problem with the IE transformation (rt in ms ÷ proportion correct) is that it assumes a linear relationship between RT and acc. That's clearly not the case. While one can often achieve a linear relationship between a predictor and RT, the relationship between a predictor and accuracy is invariably an ogive. One can make it much more linear by transforming accuracy to logit or log-odds scores (keep in mind accuracy, and in most cases even RT, are COMPLETELY arbitrary representations of what they measure). Furthermore, rt has much better statistical properties represented as responses/second than seconds/response. So, taking 1/rt in seconds would make that data more normal. Therefore, logit / inverse RT scores might be a better transform. But it's still a transform into some unknown score... I think we could call it Linearized Inverse Efficiency (or L.I.E) :)... OK, it's not actually inverse efficiency anymore since it's not an inverse rate but an accuracy corrected rate.. how about A.C.E, accuracy corrected efficiency?)
But... if you're going to go that far, why not just model the logistic regression on RT in each condition? You could then hold the RT constant for each condition (maybe the grand mean) and look at the changes in predicted accuracy across conditions. That would be a reasonable way to combine the two.
The only issue I've run into with that last one is that it's all about the leading edge of your RT distribution. You need to hack off everything after accuracy asymptotes. If what you intended to measure is the immediate response to a stimulus then that's perfectly fine. If you want to capture something about the tails of the distributions it might not be well represented, but you could look at that separately. You could keep that later data by just making the logistic regression quadratic. On the flip side, one advantage you get is that you actually make use of all of the early low accuracy RTs.
This method does require those low accuracy RTs so you do, in general, have to encourage speed in the experiment. That should also be done with any transform or model of RT and accuracy because you have to have some accuracy variance to work with.
(one thing I haven't tried, which would probably work, is just entering RT into a multilevel logistic regression of accuracy. If you include it as an interaction term you can then examine the predicted scores holding it constant.)