I also have left vocal cord paralysis, and left lateral tongue paralysis, aspirate. I was sent twice several years to two different voice specialists, who are highly regarded, for collagen injections to help strengthen my voice, but had just completed one surgery, and too much going on, and ultimately declined at that time.
I'll be looking for your follow-up post to see how it went, and hopefully it will help with the aspiration too.
Good luck!