Just a follow-up in case others see this thread.

Trying to add multiple attachments is really a PITA. However, I did discover a slightly less irritating way of getting it done...

After the first attachment is uploaded and trying to add additional ones, it is likely the "attachment upload" window will just have its spinner animating forever. Try clicking in the URL bar and press F5. Give a couple seconds, press F5 again. This seems to work for me. But how many times I need to press F5 for each attachment ranges quite a bit. Might want to have another browser opened for reading

Anyway, that's better than trying to do it the way I mentioned in the early posts.