Definitely not an expert, but your picture looks like your having horizontal hold issues.
I know that the JPac amplifies the RGB, I'm not sure if it also amplifies the sync signals. If it does, then that could be your problem!!
The other possibility is that the monitor is expecting positive sync and the AVGA card is outputting negative (or vice versa) I don't know if you can change the polarity of the AVGA sync or not, like I said I'm definitely not an expert. I've only used my AVGA card for about an hour in total, using a JPAC and I must admit I was concerned initially, because nothing was showing on the scree at all!
Eventually worked out that I needed to tweak the screen control then I could actually see something!
A fiddle with the voriz/vert size and contrast/focus and everything is sweet!!! Maybe you need to check the Hriz/Vert hold - but I guess you've already played with them.
Another option is that your monitor doesn't handle the sync frequency you're outputting. I guess you are using one of the 15KHz resolutions, if not I'd force one of them and give that a try.
Sorry I couldn't help any more....
Trev