How do you leverage a good transcript in PhD admissions?
As you stated, the lack of research experience is a problem.  When your application is being reviewed, above all, the committee will be looking for evidence that you will be able to perform impactful, independant research. 

The specifics of your industry experience and design projects will vary how much you can 'leverage' them.  Your good grades, while helpful in demonstrating your engineering knowledge and dedication, do not provide much beyond that.  If, in your industry or design projects, you had to investigate or solve a problem, I would try to emphasize them in your statement of purpose/personal statement. A specific example where you experimentally solved something could do you a lot of good.

I would not discount your research at a lab even if it was outside your field. It is direct evidence that you can perform such after all. Depending upon when you performed this research, it could even form a logical flow of why you are choosing to pursue a PhD (had the first structured experience of research at (x) but field wasn't a good fit because of (x), had several chances to do applied engineering work which was great because of (x) but was constrained and lacked (research), combined = PhD in engineering).

As the next typical round of applications will be this fall, it looks like you may have a summer to fill in some of this gap. It is critical that, if at all possible, you find a research position in engineering or a related field for these couple months.  It would be difficult to justify how interested you are in research and a PhD if you used your time to take another typical industry internship.

As for your last statement, you are obviously a weaker candidate because you have less evidence of your ability to do research. I certainly wouldn't call you an outsider, however, and industry experience, especially for an engineering student, is not uncommon. Funding will be highly dependant upon the university and your eventual advisor. Some provide departmental funding for the first year, giving you a chance to find an advisor after admittance and for one or both of you to secure a fellowship/grant. Some are fully funded. Some are much more dependant on pre-admittance contact and an interested potential advisor with an existing grant. I don't see how your work history would affect the issue of funding any differently than it would your admission process.