Why are you tilted in Asian bonds? Why not use an international bond? I'm assuming you want to minimize exposure Euro's problems.
The tilt toward Asian bonds isn't terribly high. I rebalance every year or so across US, Asia, Europe and "other" markets and there's always something left over that doesn't fit "neatly" and I tend to throw it into Asian exposure is all. So the tilt isn't huge. Most of my exposure to Asia comes from deliberate allocation, I just think a diversified portfolio needs a good dose.
I have looked at "international" bond index funds but this is where it pays to read the prospectus - many of them are basically Euro bond funds or a combination of that and US Treasuries for uninvested cash. I once ran across one purported "international" fund that was 20% in European investments and 80% US Treasuries! UST's aren't necessarily bad but you do need to know the extent of your exposure to them.
If you seriously pursue a globally diversified portfolio, prospectuses must be read. "International" is almost never "everything but the US". It's usually just Europe. Sometimes they throw in Japan (home of the Great Stagnation) too but in general if a fund invests in Asian nations it explicitly says so in the fund name.
But I don't spend a lot of time sweating small differences, basically it's divided roughly according to the size of each economy and making sure the prospectus indicates that they really are investing as expected.