You're right in that if you are paying for an engineering graduate degree, you are doing something wrong.
When I applied to graduate school, I had several options at my state university for funded programs. Several were in engineering, but large (relative) stipends were available for folks in physics, cell phys, and chemistry, as well as some odd-balls like physical chemistry. These all require that students do the "plan A" option, i.e., thesis based masters. When you check into the schools, look for this distinction, and you might find more that offer student funding (in addition to RA work, you may be asked to teach at least one semester).
Don't back away too quickly from the engineering programs. If your biotech program was math intensive, then you may only need a few additional classes to meet the pre-reqs. Also, many of the pre-reqs are offered as UG/Grad classes, and you can satisfy the pre-reqs while earning graduate elective credits at the same time. But there is certainly the possibility of having too much to do in only two years.
You might run into problems with graduating on time, however, with ANY thesis based masters program. Since MSTPs are not as willing to allow deferals, you might have to pass on an admission just to finish your chemistry thesis. That would be horrible. Its real easy to slack around for 18 months, then find yourself in some serious $hit when it is time to put the thesis together. Even if you drop the program, all your thesis credits turn to F's and the goal of using the MS to boost admission chances now has turned into a large burden. Just be careful
