You can add synthetic and regular oil together without any problems WHATSOEVER. 30 years ago, there were problems with mixing them, but not anymore.

It's not thinner either. You use 10w-30 for 10w-30, not a higher weight oil. Just use whatever weight you would use normally.

Yes, in an older engine, there might be deposits, blocking up potential leaks. So putting a oil with more detergents in it will clean up those deposits, and reveal leaks. But those leaks were already in your engine, but clogged with grime. Do you think that's a good thing?

Synthetic can last longer also, but remember to change the filter, or use a high mileage filter.