just so we are clear here, you will not be adding bags to your road bike will you? Not that it really matters but I just wanted to be sure.
From my riding experience, getting down from 29g.i. to 23 g.i. would be a noticeable and appreciated difference, and so your $200 option seems like the best way to go and you will see immediately how you like it.
When I ride my dropbar bike without anything on it, it still weighs a good 28lbs and I still appreciate having the stock gearing down around 25. I imagine your bike weighs less but then I am a light guy and like climbing, so your 23 or 22g.i option seems perfectly reasonable to me and fits along with my experience of what is nice to have for steep stuff.
as I'm sure you know, the only downside to the wide cassettes 11-40 or whatever is that you are going to lose some closer spacings between shifts. Look at the specific cogs you have now and compare them in gearing charts to the 11-40 and you'll see the larger jumps--but this is the price for a more comfortable and flexible gearing range that you will appreciate at times.
I would also add that its not really a problem with longer caged derailleurs to switch out at times the 11-40 back to a tighter cassette. I do it sometimes with my 9 speed stuff and there is usually no more than a very small rd adjustment to do, a small barrel adjuster turn and its done--so keep this in mind if you really do like a tighter cassette and can use it at times. Takes 10 or 15 mins to take off the cassette and check the shifting up on a stand.
I will be touring fully loaded. I did a trip last summer, and the bike as currently set up was fine, but this summer I'll be touring in mountainous terrain. Here is a picture of what I expect to be carrying, or possibly with rear panniers instead of the saddle bag.
