Would I be facing any kind of trouble in the future for leaving my degrees incomplete?
Leaving the masters unfinished isn't a huge problem. But moving from a Life Sciences Doctorate to Engineering is a big step and would need a lot of justification. You don't say which university in Europe so it is hard to guess at their reputation.
I won't predict that it is impossible, but I think you will have a hard time convincing people unless you have produces some substantial papers that are pretty technical.
Is getting an engineering doctorate in Europe an option for you instead of one in life sciences? Or some sort of joint degree.
Tough road. Uphill all the way, I think.