I don't think you can learn ASIC design again. From
what you said, your experise is on system level
design and mabye integration. FPGA is just one optional
knowledge, not very important.
As a senior engineer like you, you have to find the position
matched to your background pretty well. It will
help your career a lot. Do what you know best. There is
a lot of positions on hardware on system level. I suggest to
find the postions from startup. They don't care your English
level, they don't care your background, they just care what you
can do for them.
Get a senior position, it will be your only choice!