Yeah, I went through all of these ideas a few months back. IMO overkill and not even as good as the simple solution. If you tie a 3-4 inch diameter bubgee loop through the lift strap at the top back of the pack, and hook a tiny carabiner though the hand strap on the end of the umbrella you are done – and IMHO from testing it is the best, most stable, most adaptable solution by far, in spite of also being by far the simplest and lightest. This is basically what one guy did in one of the posted youtube vids on another umbrella thread several months back. When you see it and try it the other methods become superfluous.
You stick your closed umbrella (while walking)up through the lift-strap bungie loop until you can open it above the loop. After it is opened and resting on your pack reach/pull down and attach the carabiner at the end of the umbrella wrist strap to your hip belt somewhere. As Emeril Lagasse would say, BAM!
You can then also make any minor adjustment to its position you like. Choose which side of your head, and same side or cross-side for the belt attachment, as conditions warrant and/or according to personal preference. The strap on the umbrella is already springy, but you can adjust to you pack/body size, for instance, by changing the size of the lift strap loop bungee, and/or attaching another loop(s) to the belt (rather then attaching the carabiner directly to one of the belt straps) if you need more length to stretch the distance or want less tension, etc.
The back bottom of the umbrella rests on your pack. The coverage is low and very stable in moderate wind, just what you need for rain and sun coverage. Might not work as easily for a day pack, but probably something could be worked out to keep it from sitting right on your head. I suppose there may be a few packs/load where this doesn't work, but it works with all my packs of different sizes ranging from lightweight down to SUL.
On my set up the Birdypal (same as chrome dome but without logo) 7.8 oz, plus bungee loop and micro carabiner still less than 8 oz.