Note; My answer here is more a lot of possible solutions to the problem, and a touch of humor (I was answering in the middle of the night after long hours of typing a lesson plan for HS students). Without riding the bike, or riding along side of the owner to observe what the bike is doing, this is the best I can do. But I think it illustrates the need to know about your bike, and not rely on a shop tech or a dealer to give you the straight answers you need. Remember, they are desperately trying to sell motorcycles, but you are trying not to buy one!
A. OK - Don't Panic
First of all, you have added a lot of weight to the bike. It's not excessive from what I can see, but it is additional over what Yamaha designed the bike to carry on the front. The other thing is it's an old bike. Let's face the facts, our Viragos are aging. Just as we feel the pull of gravity and come up with little aches and pains as we age, so do our bikes. That's a fact.
Here's some possible changes you can make to help the resolve problem, short of turning her into a chopper to lighten the load (although personally, I do like the sleeker look of the chopper, over the heavier stance of the bagger)
Change the fork pre-load. I am not familiar enough with the XV920J to say how to do this, but I have heard you can do it with a couple small lengths of steel pipe that fit inside the tubes, or with ABS plastic pipe that fits the same way. You need to stiffen the front end to keep it from diving as soon as it does.
A better way, and one I will strongly recommend in spite of the cost factor (it's your life you have to value when you go into those squirely curves, after all!) is a set of Progressive fork springs to replace the weakened, aging fork springs that she came with. Look at that linked page and follow the links to find the set you need, and ultimately the price (You may want to have an ER technician standing by with a crash cart, if your heart is weak!).
You have, I gather from your post, checked the axel, bushings, steering head bearings, tension on the steering stem, etc. Have you checked the swing-arm bushings too? If not, before you buy anything or change the front end in any way, check the condition of those swing-arm bushings. They are absolutely critical to the way the bike handles. If they get bad enough, even straight roads can become an adventure in taunting death.
Another factor to consider is the total load/weight distribution on the bike at any given time. With luggage, you have to be extremely cognizant about weight distribution. You'll also want to make sure you have the right tires for what you're doing. Street tires on a bike set-up to tour is a bad thing when it comes to handling. Also, check to see if the forks are getting overstressed in turns. If they flex abnormally because of the fairing or added weight of the luggage, you may really just need an aftermarket fork brace to tie the two sides together better. This is often a really effective fix, but isn't always best because the brace can just 'band-aid' the trouble and hide other, worse problems until it's too late.
There is a lot to consider here. I wish I were able to see the bike, and ride along side of you to see what it's doing, exactly.
The shops you have been to should simply close their doors, because they have no clue as to what they are talking about. None whatsoever. From the very first day they hit the market, Yamaha's Virago has been, and continues to be, one of the absolute best handling motorcycles ever manufactured.
Additional Information: A comment to the original question by "Geo", another long time Virago rider, fairly knowledgeable Virago guy, and absolute motor head reads as follows: "OK. when I got mine as a wreck and rebuilt it it was very squirely. You can read my story on my website. The short of it is, Progressive front and rear springs ( about $225 for all three), then use 15 weight fork oil. Tapered steering bearings from partsnmore.com also helped. When I get real aggressive in the turns, I put my feet on the passenger pegs and lean forward. To give you a partial idea of what the springs will do for you, put 40 psi in the rear and 25 in the front and set your front dampener settings to 3 or 4 and the rear as high as it will go. There should be a marked improvement, but no where near what the springs did for me." and "Also, I wanted to mention the first thought I had was the same as bykrmom. Empty the trunk and saddle bags. The best place to carry extra weight is in an imaginary triangle with the three points being the two axels and the top of your helmet. Yes, I know there isn't really any open spaces there. So saddle bags and tank bags and backpacks [are] the best for keeping the balance of the bike. The Progressive front springs came with the spacers.
Tire brands also make a difference. I have Dunlop 495 in rear and [Dunlop] f11 in front.