A nice conundrum.

I certainly understand why you don't want to make any cuts or permanent changes to such an expensive bag, but in this case you might not be able to avoid it.

I think the first thing you should try, the easiest and least destructive method, is to get yourself some 1" braided elastic from your local sewing shop, and some sew-on 3/4" Velcro strips. Sew a couple of inches of Velcro onto the ends of two pieces of elastic, and try attaching them to the Velcro strips on the inside of the bag. Load it up with clothing, and see how well it holds. It may do the job for you, though I an doubtful.

Another route to try would be wider elastic. Shop around and you can find elastic in widths up to 3". Add some Velcro to the ends of two or three strips of wide elastic, and stretch them across the bag straight - top, middle, bottom - instead of the X pattern. This will give you a 3" wide strip of Velcro holding each strap in place, which will hold more firmly than the ends of 1" strips going across in an X pattern.

If those options fail you, then it will be time to throw in the towel and make physical alterations to the bag itself. The simplest method to give you the straps you want, in the location you want, will be to hand-stitch some elastic straps to the corners of the liner. If you make 4 pieces, attach the ends to the 4 corners, and add Velcro to the opposite ends, they will all meet in the middle of the space and Velcro together.

The most drastic method, but the strongest and most secure, would be to actually drill holes through both the outside material of the bag and the liner, and use machine screws and locking nuts to add elastic straps to the inside. The beauty of this method, which I have used on cheaper bags myself, is its versatility; if your elastic becomes stretched or torn, you can swap it out for new pieces by simply unscrewing the lock nuts. Likewise, you can swap the elastic for webbed straps later, and you can use these same screws and nuts to add components to the outside of the bag, as well (such as a water bottle holder or a shoulder strap). The important part here is to find machine screws that are juuuuuuuuuust the right length, so that the ends don't protrude too far into the interior of the bag where they might catch on your clothing.